2019 Gauss 8 Problem 22

Rich chooses a 4-digit positive integer. He erases one of the digits of this integer. The remaining digits, in their original order, form a 3-digit positive integer. When Rich adds this 3-digit integer to the original 4-digit integer, the result is 6031. What is the sum of the digits of the original 4-digit integer?

\textbf{(A)}\ 18\quad \textbf{(B)}\ 20\quad \textbf{(C)}\ 22\quad \textbf{(D)}\ 19\quad \textbf{(E)}\ 21

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.