### Solving an equation in multiple variables

I have this equation :
sqrt((b-a)^2 + (B-A)^2) == A+B and i would like to have it solved to b-a=+- 2 * sqrt(AB) in sage. Right now I have the following code but it doesn't really output what I want. I just get

A^2 - 2*A*B + B^2 + a^2 - 2*a*b + b^2 == A^2 + 2*A*B + B^2

and I don't know how to make sage solve it further.

my code:

~~var('a,b,c,A,B,C')
~~var('a,b,c,A,B,C')

eq1 = (sqrt((b-a)^2 + (B-A)^2) == ~~A+B)
(eq1^2).expand()~~A+B)

(eq1^2).expand()

Thanks in advance