In solving these problem I find it helpful to use the following table: 10 rows of digits, N columns for each letter. Put a checkmark in the cell when you know the value of a letter. Put an X in a cell when you know that a letter can't have this value. After putting a checkmark in a cell you can put Xs in all other cells in the same row and column.
E.g. based on D*D=D or D+10 we know that D can't be 2,3,4, etc. Based on the fact that D is the first digit we know it's not 0. This leaves not that many choices for D.
See attached example.
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