2025 AMC 8 Problems

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$1)$ Let $m$ and $n$ be $2$ integers such that $m>n$. Suppose $m+n=20$, $m^2+n^2=328$, find $m^2-n^2$.

$\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340$


$2)$