To begin with, C must be less than 4, otherwise the sum would have 7 digits. If C is 3, then R is 9 and C+O+O+E < E, which is impossible, so C cannot be 3. This leaves only two options for C (either 1 or 2). If you try C=1 with various values for O, you can prove that C cannot be 1. Repeat with C=2 to find the solution.