Newtonian Solution to Compton Scattering

[Partyzan]

Homework Statement

I need to derive the Compton scattering formula using Newtonian mechanics, I have it done in relativistic mechanics but can't get the Newtonian version.

Homework Equations

the solution to the relativistic equation is

1=mc^2(1/E2-1/E1)+cos(theta)

for Newtonian mechanics:

1=mc^2(1/E2-1/E1)+cos(theta)-(E1-E2)^2/2E1E2

The Attempt at a Solution

i have no idea where to get started for the Newtonian solution

 

[Partyzan]

i have the relativistic solution, but if i could just get pointed in the right direction for the Newtonian solution, that would be amazing.