1955 AHSME Problem 19

Two numbers whose sum is 6 and the absolute value of whose difference is 8 are roots of the equation:

\begin{array}{l} \textbf{(A)}\ x^2-6x+7=0\qquad\textbf{(B)}\ x^2-6x-7=0\qquad\textbf{(C)}\ x^2+6x-8=0\\ \textbf{(D)}\ x^2-6x+8=0\qquad\textbf{(E)}\ x^2+6x-7=0 \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.