Help solving a digit and word code problem/riddle: sum of four "ONE"s is "TEN" 
Replace each letter by a digit. The same digit must represent each
letter, and no beginning letter of a word can be zero. No two letters can
be the same number. Find the digits represented by the letters 'O',
'N', 'E', 'T'.
O N E
O N E
O N E
O N E
=====
T E N

I have tried this, but I can't seem to crack it. It doesn't make sense to me. Can anyone help with this?

'ONE' represents the number $100 \times O + 10 \times N + E$, just as $781$ represents $7 \times 100 + 8 \times 10 + 1$. This is what the decimal position
system is. 
So 'ONE' added 4 times to itself is just $400 \times O + 40 \times N + 4E$ and this should represent the same number as 'TEN' = $100 \times T + 10\times E + N$.
This means 'N' is a the final digit of a multiple of $4$, so $2,4,6,8,0$ are the options for 'N'. For more hints, see the comments.   
