Answer
$-6, 5$
Work Step by Step
1. Let the two numbers be $x,y$, we have $\begin{cases} x+y=-1 \\ x^2+y^2=61 \end{cases}$
2. The first equation gives $y=-x-1$
3. Use substitution in the second equation, we have $x^2+x^2+2x+1=61$, $x^2+x-30=0$ or $(x+6)(x-5)=0$
4. We have $x=-6,5$ and $y=5,-6$
5. Thus, the two numbers are $-6, 5$
