If we rewrite the equation we get the product $E\times I\times G
\times H\times T = T\times W \times O\times F\times O
\times U \times R$.
There are $10$ different letters here, so each number from $0$ to
$9$ must be represented by one of the letters. So one letter is
$0$. Any product where this letter appears is $0$. Hence both sides
must include this letter. The only letter on both sides is $T$.
Hence $T=0$ and the product $T\times H\times R \times E
\times E =0$.
This problem is taken from the UKMT Mathematical Challenges.