Compton scattering, formulae question

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Homework Statement


An X-ray source of wavelength gamma is directed at a sample; determine the maximum speed of scattered electrons.

Homework Equations



KE=(\gamma-1)mc2=hc/\lambda - hc/\lambda'

The Attempt at a Solution



I've been provided with the solution using the formula above, however it looks like it's Eincident - Escattered ---or in other words initial minus final...isn't convention final-initial? Why do we subtract initial minus final in this case?
 
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The final is subtracted because the scattered photon will have a lower energy than the incident photon (since some of it has gone to the electron).
 
Apply conservation of energy to the situation.

This question really doesn't belong in the advanced physics section.
 
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