1957 AHSME Problem 23

The graph of x^2 + y = 10 and the graph of x + y = 10 meet in two points. The distance between these two points is:

\textbf{(A)}\ \text{less than 1} \qquad \textbf{(B)}\ 1\qquad \textbf{(C)}\ \sqrt{2}\qquad \textbf{(D)}\ 2\qquad\textbf{(E)}\ \text{more than 2}

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