Systems, Matrices, and Determinants · Challenge problem

A message is encoded two numbers at a time using the matrix $E=\begin{bmatrix}1&2\\1&3\end{bmatrix}$: a plaintext pair $(p_1,p_2)$ becomes the ciphertext $E\begin{bmatrix}p_1\\p_2\end{bmatrix}$. A ciphertext pair is $(16,21)$. Find $p_1+p_2$.