Sum of Possible Absolute Differences

If $x^2 + y^2 = 25$ and $xy = 24$, find the sum of all possible values of $|x^2-y^2|$. The answer is in the form $a\sqrt{b}$ for where $a$ and $b$ are positive integers, and $b$ is square-free. Input the answer as the sum $a+b$.