Math Problem Solver

The numbers are $6$ and $-2$.

The sum of $n_{1}$ and $n_{2}$ is $4$, and their difference is $8$. This translates to the two equations: $$\begin{aligned}n_{1} + n_{2} &= 4\\n_{1} - n_{2} &= 8\\\end{aligned}$$ Adding the two equations together yields:$$\begin{gather*} 2 n_{1} = 12\\ n_{1} = 6\end{gather*}$$ Substituting $6$ for $n_{1}$ into $n_{1} + n_{2} = 4$ results in $6 + n_{2} = 4$, so $n_{2} = -2$.