2021 AMC 12B Problem 10

Two distinct numbers are selected from the set \{1,2,3,4,\ldots,36,37\} so that the sum of the remaining 35 numbers is the product of these two numbers. What is the difference of these two numbers?

\textbf{(A) }5 \qquad \textbf{(B) }7 \qquad \textbf{(C) }8\qquad \textbf{(D) }9 \qquad \textbf{(E) }10

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