One number is 6 more than anouther number. the sum of their squares is 90

Let x = greater number
      y = smaller  number

(1)
(1)

(2)
We'll substitute y in (1) to (2)
(2)
    
    
    
    
    
 x - 9 = 0        or      x + 3 = 0
      x = 9                        x = -3
and
 y = x - 6                  y = x - 6
 y = 9 - 6                  y = -3 - 6
 y = 3                        y = -9

Therefore, the two numbers can be 9 and 3 or -3 and -9.