In the context of a numerical simulation I have normally distributed random variables $A$ and $C$. These variables are based on real data. I know that there is a distribution $B$ where $A + B = C$.
Let $A = N($$\mu_a$,$\sigma_a$)
Let $C = N($$\mu_c$,$\sigma_c$)
$\sigma_c > \sigma_a$
If I only know $C$ and $A$, how could I go about calculating $B$ using some numerical method?