The difference of two positive numbers is 6 and the sum of their squares is 90. Find the numbers?

let the numbers be x and y with y > x > 0

y - x = 6 ..1

y^2 + x^ 2 = 90 ..2

we know (y-x)^2 + (y+x)^2 = 2 (y^2 + x^2)

or 6^2 + (y+x)^2 = 2 * 90 = 180

(y + x) ^2 = 180- 36 = 144

or y + x = 12 .. 3 ( as y + x > 0)

from 1 and 3 we get x= 3 and y = 9