If $x^2-y^2=91$ and $x+y=13$, where $x$ and $y$ are positive integers, then $x-y$ equals:

Factorise: $x^2-y^2=(x+y)(x-y)$, so $13(x-y)=91$ and $x-y=91÷13=7$. Solving the pair gives $x=10$ and $y=3$, and indeed 100 − 9 = 91. Subtracting instead of dividing gives 91 − 13 = 78, a typical slip.