Let
\[f(n) = \left\{ \begin{array}{cl} n^2-2 & \text{ if }n<0, \\ 2n-20 & \text{ if }n \geq 0. \end{array} \right.\]
What is the positive difference between the two values of $a$ that satisfy the equation $f(-2)+f(2)+f(a)=0$?
The positive diffference is 14.