I know how to prove this using real numbers, for instance knowing P(A)= .5 and P(B)=. 2 and (AB)= .1 which is .5+.2-2(.1)= .5, but I have no idea how to write this using notation. Any ideas?

You probably mean

A U B - AB = (A^c B) U (AB^c), or

P(A U B) - 2P(AB) = P(A^c B) + P(AB^c).

Venn diagrams are a useful tool that help visualize the situation here.

https://www.cut-the-knot.com/LewisCarroll/VennClick.shtml

You can use, say,

A^c B = B - A = B - AB.

Also,

(B-AB)·(AB) = empty and (B - AB) U AB = B.

So that

P(A^c B) = P(B) - P(AB).

Similarly,

P(AB^c) = P(A) - P(AB).