Word Square

Since we have distinct digits, let's focus on the low sums as they restrict the possibilities.
From $T + W + O = 6$ , we know that $\{ T, W, O \} = \{ 1, 2, 3 \}$ .
From $T + O + E = 7$ , we know that $\{ T, O, E \} = \{ 1, 2, 4 \}$ . Hence $W = 3, E = 4$ and $\{ T, O \} = \{ 1, 2 \}$ .
From $E + Y + E = 17$ , we get that $Y = 9$ .
From $W + A + Y = 17$ , we get that $A = 5$ .
From $O + R + E = 11$ , we get that $O + R = 7$ . If $O = 2$ then $R = 5$ which is not possible since $A = 5$ . Thus $O = 1$ , $R = 6$ , $T = 2$ .

We have $\overline{TOWER} = 21346$ .