Let $m$ and $n$ satisfy $mn=7$ and $m+n=8$. What is $|m-n|$?
I notice that $m$ and $n$ are the solutions of the quadratic equation $x^2-8x+7=0$, which I can factor as $(x-7)(x-1)=0$. So $m$ and $n$ are either 7 and 1, or 1 and 7, depending on the order. Either way, $|m-n|=|7-1|=6$.

