One convention in these puzzles is that the numbers given don't start with a zero. So the S and the M cannot be zero.

You shouldn't have to guess what the "M" stands for. Logical thinking is all that is required. Once you know that one, you can reason what the S is, and what the O must stand for.

You have three equations with an E;
D+E=(10+)Y
N+R=(10+)E
E+O=(10+)N
Two of these contain an N as well. By comparing those relations you can make some more educated guesses as to what the E and the N cannot stand for.

Continue from there.

Whymme