Question 606961
if one integer is x 
the other will be x-8

x^2+(x-8)^2=610

x^2+x^2-16x+64=610

2x^2-16x=546

/2
x^2-8x=273

x^2-8x-273=0

x^2-21x+13x-273=0

x(x-21)+13(x-21)=0
(x-21)(x+13)=0

x=21 OR -13

The integers are positive 
so the numbers are 21 & 13