$4 \cdot 191$ The sum of the sum, difference, product, and quotient of two integers is 450, find these two numbers.
［Solution］Let these two integers be $x, y$, then
$$
(x+y)+(x-y)+x y+\frac{x}{y}=450 \text {, }
$$

From (1), we get $\frac{x}{y}$ is an integer.
Transform equation (1) into $\frac{x}{y}(y+1)^{2}=450$.
Notice that $450=1 \times 2 \times 3 \times 3 \times 5 \times 5$,
Thus, from equation (2), the unknowns $x$ and $y$ are:
$$
\begin{array}{l}
(28,14),(100,2),(72,4),(-32,-16),(-200,-4), \\
(-108,-6),(-900,-2) .
\end{array}
$$