10. From the set $\{1,2, \cdots, 37\}$, select two numbers such that the sum of the remaining 35 numbers is the product of these two numbers. Then the difference between the two numbers is ( ).
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
10. E.

Let the two numbers drawn be $x, y(x<y)$. From the problem, we have
$$
\begin{array}{l}
\frac{37(37+1)}{2}-x-y=x y \\
\Rightarrow x y+x+y=703 \\
\Rightarrow(x+1)(y+1)=x y+x+y+1 \\
\quad=704=2^{6} \times 11 \\
\Rightarrow(x+1, y+1)=(22,32) \\
\Rightarrow(x, y)=(21,31) \\
\Rightarrow y-x=10 .
\end{array}
$$