Answer
One pair of numbers is -6 and -4. The other pair is 4 and 6.
Work Step by Step
$$x^2+(x+2)^2=52$$
$$x^2+x^2+4x+4=52$$
$$2x^2+4x-48=0$$
$$x^2+2x-24=0$$
$$(x+6)(x-4)=0$$
$$x=-6,4$$
One pair of numbers is -6 and -4. The other pair is 4 and 6.