\(R=8\Rightarrow O=4 \vee O=9\).
If \(O=4\Rightarrow T=2 \vee T=7\).
But none two three-digit numbers starting with 2 give a four digit number as a result when added up, therefore \(T=7 \Rightarrow F=1\)
There's \(W\) and \(U\) left.
\(W\) can't be equal to 0, because this would mean also \(U=0\) and each letter is supposed to represent a different digit.
\(W\) can't be equal 1, because \(F=1\).
\(W\) can't be equal 2, because \(U\) would be equal 4, and already \(O=4\)
\(W=3\) seems to be a fine digit, because then \(U=6\) and 6 hasn't been used yet.
So \(FOUR=1468\).
It's possible that there are more solutions (for the rest values of \(W\) and for \(O=9\), but I don't want to check for them :D
And sorry for my laconic explanation. I suck at this, especially in English :P
