Question 848059
x+y = 18
x^2+y^2 = 164


x = (18-y)

(18-y)^2 + y^2 = 164

324 - 36y + y^2 + y^2  =164

324 - 36y + 2y^2 = 164

2y^2 -36y + 160

2(y^2 -18y + 80)

(y-10)(y-8)

If y = 8

x+8 = 18

x = 10

If y= 10

x+10 = 18

x= 8

^ that seemed redundant, but it's entirely possible we could have had more than one pair of solutions.

Anyway, this means the numbers are 8 and 10.