You add vectors by placing the vectors one after another, $\overrightarrow{n}+\overrightarrow{v}$. The result is a vector that begins in the starting point of the first vector, and ends in the end point of the last vector.

You subtract vectors by adding the vectors one after another. But, before you add the last vector, you have to reverse it.

$$\overrightarrow{n}-\overrightarrow{v}=\overrightarrow{n}+\overrightarrow{-v}.$$