diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 888e943488953..db76f5c51752f 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -1017,10 +1017,10 @@ def rank(
 
 def checked_add_with_arr(
     arr: npt.NDArray[np.int64],
-    b,
+    b: int | npt.NDArray[np.int64],
     arr_mask: npt.NDArray[np.bool_] | None = None,
     b_mask: npt.NDArray[np.bool_] | None = None,
-) -> np.ndarray:
+) -> npt.NDArray[np.int64]:
     """
     Perform array addition that checks for underflow and overflow.
 
@@ -1098,7 +1098,12 @@ def checked_add_with_arr(
 
     if to_raise:
         raise OverflowError("Overflow in int64 addition")
-    return arr + b
+
+    result = arr + b
+    if arr_mask is not None or b2_mask is not None:
+        np.putmask(result, ~not_nan, iNaT)
+
+    return result
 
 
 # --------------- #
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 1dfb070e29c30..122b61e2e351d 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1104,8 +1104,12 @@ def _add_datetimelike_scalar(self, other):
             return DatetimeArray(result)
 
         i8 = self.asi8
-        result = checked_add_with_arr(i8, other.value, arr_mask=self._isnan)
-        result = self._maybe_mask_results(result)
+        # Incompatible types in assignment (expression has type "ndarray[Any,
+        # dtype[signedinteger[_64Bit]]]", variable has type
+        # "ndarray[Any, dtype[datetime64]]")
+        result = checked_add_with_arr(  # type: ignore[assignment]
+            i8, other.value, arr_mask=self._isnan
+        )
         dtype = DatetimeTZDtype(tz=other.tz) if other.tz else DT64NS_DTYPE
         return DatetimeArray(result, dtype=dtype, freq=self.freq)
 
@@ -1146,7 +1150,6 @@ def _sub_datetimelike_scalar(self, other: datetime | np.datetime64):
 
         i8 = self.asi8
         result = checked_add_with_arr(i8, -other.value, arr_mask=self._isnan)
-        result = self._maybe_mask_results(result)
         return result.view("timedelta64[ns]")
 
     @final
@@ -1168,14 +1171,13 @@ def _sub_datetime_arraylike(self, other):
 
         self_i8 = self.asi8
         other_i8 = other.asi8
-        arr_mask = self._isnan | other._isnan
-        new_values = checked_add_with_arr(self_i8, -other_i8, arr_mask=arr_mask)
-        if self._hasna or other._hasna:
-            np.putmask(new_values, arr_mask, iNaT)
+        new_values = checked_add_with_arr(
+            self_i8, -other_i8, arr_mask=self._isnan, b_mask=other._isnan
+        )
         return new_values.view("timedelta64[ns]")
 
     @final
-    def _sub_period(self, other: Period):
+    def _sub_period(self, other: Period) -> npt.NDArray[np.object_]:
         if not is_period_dtype(self.dtype):
             raise TypeError(f"cannot subtract Period from a {type(self).__name__}")
 
@@ -1183,8 +1185,8 @@ def _sub_period(self, other: Period):
         # of DateOffsets.  Null entries are filled with pd.NaT
         self._check_compatible_with(other)
         asi8 = self.asi8
-        new_data = asi8 - other.ordinal
-        new_data = np.array([self.freq.base * x for x in new_data])
+        new_i8_data = asi8 - other.ordinal  # TODO: checked_add_with_arr
+        new_data = np.array([self.freq.base * x for x in new_i8_data])
 
         if self._hasna:
             new_data[self._isnan] = NaT
@@ -1192,7 +1194,7 @@ def _sub_period(self, other: Period):
         return new_data
 
     @final
-    def _add_period(self, other: Period):
+    def _add_period(self, other: Period) -> PeriodArray:
         if not is_timedelta64_dtype(self.dtype):
             raise TypeError(f"cannot add Period to a {type(self).__name__}")
 
@@ -1225,8 +1227,6 @@ def _add_timedeltalike_scalar(self, other):
         inc = delta_to_nanoseconds(other, reso=self._reso)  # type: ignore[attr-defined]
 
         new_values = checked_add_with_arr(self.asi8, inc, arr_mask=self._isnan)
-        new_values = new_values.view("i8")
-        new_values = self._maybe_mask_results(new_values)
         new_values = new_values.view(self._ndarray.dtype)
 
         new_freq = None
@@ -1262,10 +1262,6 @@ def _add_timedelta_arraylike(
         new_values = checked_add_with_arr(
             self_i8, other_i8, arr_mask=self._isnan, b_mask=other._isnan
         )
-        if self._hasna or other._hasna:
-            mask = self._isnan | other._isnan
-            np.putmask(new_values, mask, iNaT)
-
         return type(self)(new_values, dtype=self.dtype)
 
     @final
@@ -1309,11 +1305,11 @@ def _sub_period_array(self, other: PeriodArray) -> npt.NDArray[np.object_]:
         self = cast("PeriodArray", self)
         self._require_matching_freq(other)
 
-        new_values = checked_add_with_arr(
+        new_i8_values = checked_add_with_arr(
             self.asi8, -other.asi8, arr_mask=self._isnan, b_mask=other._isnan
         )
 
-        new_values = np.array([self.freq.base * x for x in new_values])
+        new_values = np.array([self.freq.base * x for x in new_i8_values])
         if self._hasna or other._hasna:
             mask = self._isnan | other._isnan
             new_values[mask] = NaT
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index b6d21cd9dac54..cab9a8a565145 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -733,8 +733,6 @@ def _addsub_int_array_or_scalar(
         if op is operator.sub:
             other = -other
         res_values = algos.checked_add_with_arr(self.asi8, other, arr_mask=self._isnan)
-        res_values = res_values.view("i8")
-        np.putmask(res_values, self._isnan, iNaT)
         return type(self)(res_values, freq=self.freq)
 
     def _add_offset(self, other: BaseOffset):