2016 Gauss 8 Problem 25

In the table, the numbers in each row form an arithmetic sequence when read from left to right. Similarly, the numbers in each column form an arithmetic sequence when read from top to bottom. What is the sum of the digits of the value of x?

\begin{array}{|c|c|c|c|c|}\hline \phantom{00} & \phantom{00} & \phantom{00} & \phantom{00} & 18 \\\hline & 43 & & & \\\hline & & 40 & & \\\hline & & & & \\\hline x & & & 26 & \\\hline \end{array}

(An *arithmetic sequence* is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.)

\textbf{(A)}\ 5\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 10\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 13

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.