Answer:
[tex]x^2-y^2=\pm35[/tex]
Fast and loose:
The difference being positive tells you that [tex]x>y[/tex]. Now try staring at the product for a while, and think of all possible combinations. It's either 6,1 and 3,2, -2,-3, -1,-6 Now, the 3/2 pair both give 1, so no good. 6-1 and [tex]-1-(-6)[/tex] are indeed 5.
Rigorously:
if [tex]x-y=5[/tex] it means [tex]x=5+y[/tex], let's replace in the second
[tex](y+5)y=6\\y^2+5y-6= (y-1)(y+6)=0[/tex]
From this we get either [tex]y=1; x=6[/tex] or [tex]y=-6; x=-1[/tex] . At this point is just replacing either pairs to get the result.
The result!
At this point we just have to crunch numbers:
[tex]6^2-1^2= 36-1=35[/tex] OR
[tex](-1)^2-(-6)^2=1-36=-35[/tex]
