Five Across, Four Down

A camera's calibration routine writes a test patch of pixels into a $4 \times 5$ matrix $P$ — 4 rows and 5 columns. Rows and columns are numbered starting at $1$, and the brightness stored at row $i$, column $j$ is given by the rule

$P_{i,j} = 2i + 3j$

So, for example, the pixel in row $1$, column $4$ holds $2(1) + 3(4) = 14$.

The technician adds up one full row and one full column of the patch. Compute the total brightness of row 3 and the total brightness of column 2, then report

$(\text{total of row } 3) - (\text{total of column } 2)$

Give your answer as an exact whole number.