2016 Cayley Problem 18

When three positive integers are added in pairs, the resulting sums are 998, 1050 and 1234. What is the difference between the largest and smallest of the three original positive integers?

\textbf{(A)}\ 262\quad \textbf{(B)}\ 248\quad \textbf{(C)}\ 224\quad \textbf{(D)}\ 250\quad \textbf{(E)}\ 236

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 Cayley contests here.