The diffraction patterns are same (or close enough for our purposes anyway). This means that the electron and the x-ray will have the same wavelength and the same momentum. You are correct in saying that they will not have the same energy.
So we know that the energy of the x-ray will be:
(as this is the case for all forms of EMR)
So we need to find wavelength of the x-ray. This is the same as wavelength of the electron.
The wavelength of the electron is:
Great, now we need to find the momentum of the electron.
Note that we have to convert Ek from electron volts to joules.
Just substitute it into the equation and you should be good to go.
You get the correct answer if you use
I'm not sure why it doesn't work if you rearrange the 
for 
(
). I've done that on other exams before.
Looking back, when I did VCAA 2010, I went with but I'm not sure why I chose that equation over the other - I didn't note down my reasoning somewhere either 
. I'll investigate this further.
When you have the momentum, you can find the wavelength.
Then you can find the energy of x-ray. Be sure to use the correct Planck values throughout. If there's momentum involved, you use the J s value - if you need to find eV you use the eV s value.
edit: So that equation didn't seem to work was because it looks like it is wrong (square root of mv^2 is not mv - algebra fail lol) :/. I looked back at the trial exams I was using it for - I only used it in a qualitative fashion. Glad that I noticed I was making a simple mistake :/
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