Two numbers differ by two units and the sum of their squares is 580. What are those numbers?

N and n+2 are the numbers and the sum of their squares is 580 so:

n^2 + (n+2) ^2=580

n^2+n^2+4n+4=580

2n^2+4n-576=0

2 (n^2+2n-288) = 0

2 (n^2+18n-16n-288) = 0

2 (n (n+18) - 16 (n+18)) = 0

2 (n-16) (n+18) = 0

So there are two solutions ...

16 and 18 or

-16 and - 18