It solves a system of equations like the following:
$\psi(x)-\psi(x+y) = c1$ $\psi(y)-\psi(x+y) = c2$
For newton's method we are using the following iterations:
$\psi(x_new) = \psi(x_old+y_old) + c1$ $\psi(y_new) = \psi(x_old+y_old) + c2$
The script gives the following output: