probability - Random variable with expectation equal to itself

I read from a book that
$E(X) = X$ iff there is a constant $C$ such that $P(X=C) = 1$. But how to prove it? Thanks a lot for your help!

Answer

I am sorry, but E(X) = X does not make sense. E(X) is a number, X is a random variable. It could only make sense if the random variable X could only take one possible value.
Perhaps this is also partially the answer to your question.