One number is six more than another number. The sum of their squares is 90.

First number: x
Second: x + 6
(x)^2 + (x + 6)^2 = 90
x^2 + x^2 + 6x + 6x + 36 = 90
Simplify more
2x^2 + 12x + 36 = 90
2x^2 + 12x - 54 = 0
2(x + 9)(x - 3) = 0
You know that x = -9, and 3
The first number is 3, the other -9

Google it that might work