Answer
$(5,2), (-5,-2)$
Work Step by Step
1. Let the two numbers be $x, y$, based on the given conditions, we can get:
$\begin{cases} xy=10 \\ x^2-y^2=21 \end{cases}$
2. The 1st equation gives $y=\frac{10}{x}$, use it in the 2nd equation to get $x^2-100/x^2=21$ or $x^4-21x^2-100=0$ or $(x^2+4)(x^2-25)=0$ thus $x=\pm5$
3. Use the 1st equation again to get the solution(s) $(5,2), (-5,-2)$
