Solving a system of Quadratic Equations

I am doing a cryptography program in python...I'll give you the summary.

It consists in reading a random phrase, like: "HELLO". Then it assigns it's respective ASCII equal like:

H=72, E=79.

Then, using Pythagoras' Theorem, it creates two numbers C1 and C2, like this:

C1 = sqrt(A^2 + (A+B)^2);
C2= sqrt(B^2 + (A+B)^2)

where, in this case A = H and B = E. That would be the encryption part, but I am having problems solving the system, which will act as the decryptor.

Now here is the question:

How can I solve this system using python?

C1 = sqrt(A^2 + (A+B)^2); 
C2 = sqrt(B^2 + (A+B)^2);

Of course only C1 and C2 are known.

Do I need a new module? Which one?

via Chebli Mohamed