The next letter we can solve for is R.
Since we are adding the letter E to the number 0 and not getting the letter E in the hundreds column, we know we are carrying over a 1 from the tens column. That means that N must be one greater than E.
Looking at the 10s column (N plus R), and knowing that N is one greater than E, the only way that can happen is that R is either a 9 and when we add that to the N to get one less than N or an 8 to the N plus carry one from the singles column to get one less than N. Since 9 is already taken, that means that R is an 8.
At this point, the solution would look like this:
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