Well, since C has to be twice E, the only single digits that are twice
another single digit are 2, 4, 6 and 8. No matter how many digits
there are in a number, if you square it, the last number is the last
digit of the square of the last digit of the number you're squaring.
(for example, the last digit of 559 squared must be 1, since 9x9 is
81). So the only number out of those four whose last digit of its
square is half the number itself is 8. Therefore, C must be 8, and E
must be 4.
After that I crapped out, you're left with possibilities: 88804, 88814,
etc., and I just plugged them into a calculator. Let me know if there's
a more elegant method for figuring out the other digits.