Question 894315
I just answered this a few minutes ago.  Notice what question is asked!  

You do not need to try to solve for both x and y.


Two numbers, x and y.
{{{x^2+y^2=256}}} and {{{(x+y)^2=784}}}.
The second equation is {{{x^2+2xy+y^2=784}}}.


Subtract the circle equation from the second equation:
{{{x^2+2xy+y^2-x^2-y^2=784-256}}}
{{{2xy=528}}}
{{{highlight(xy=264)}}}, the answer.