Pick any number with at least three different digits. Jumble the digits however you want to create a different number. Take these two numbers and find their difference. Their difference is your new number. Pick a non-zero digit in your new number and remove it. Give me the rest of the digits in any order you please. From this, I can work out what digit you removed.

How do I find your digit? Why does this work? Prove it.

The idea for this puzzle was taken from a mindreading program here.