Answer
One pair of numbers is -11 and -9. The other pair of numbers is 9 and 11.
Work Step by Step
$$x^2+(x+2)^2=202$$
$$x^2+x^2+4x+4=202$$
$$2x^2+4x-198=0$$
$$x^2+2x-99=0$$
$$(x+11)(x-9)=0$$
$$x=-11,9$$
One pair of numbers is -11 and -9. The other pair of numbers is 9 and 11.