SEND + MORE = MONEY
Each letter represents a single digit number.
No two letters represent the same number. (Ex: if M=1 the no other letter in the problem can equal 1)
So far we've figured out that M=1, O=zero, and S is either 8 or 9
This is a very interesting problem, but we're a bit stuck and don't know where to go from here.
Using your assumptions: $M=1, \ O=0, \ S=9$, by method of exhaustion of setting $E$ to be $2,3,4,\dots$ I got one (perhaps not the only) solution: $$ \textrm{SEND} = 9567, \textrm{MORE} = 1085, \textrm{MONEY} = 10652. $$
From your assumptions I deduced that $R=8$, because we would have to transfer $1$ in order to have $E\neq N$. Then you use the fact that when transferring the $1$ to the hundreds, you have $E=N+1$, and by exhausting digits, you find that for $E\in \{2,3,4\}$ there are no solutions which would yield that every letter is a unique digit. Then with $E=5$ you get this solution.