I learnt how Russell's paradox can be derived from Cantor's theorem here, but also from S C Kleene's Introduction to Metamathematics, page 38.
In his book, Kleene says that if $M$ is set of all sets, then $\mathcal P(M)=M$ but since this implies $\mathcal P(M)$ has same cardinality as $M$, so there exists a subset $T$ of $M$ which is not element of power set $\mathcal P(M)$. This $T$ is desired set for Russell's paradox, i.e., it is the set of all sets which are not members of themselves.
I can't understand how $T$ is desired set for Russell's paradox. Also, how is Kleene's argument similar to the quora answer?