(ABC)^2=CCCDE

(ABC)^2=CCCDE each letter stands for a different didgit, and C is
twice E. what does each letter stand for???

By writing out all squares and using that C=2E, you quickly get AB8^2=888D4. Since 888D4 is just under 300^2 it quickly follows that 298^2=88804.
So:

A=2
B=9
C=8
D=0
E=4