2. (10 points) In the addition problem below, eight different letters each represent one of the digits from 2 to 9, with the same letter representing the same digit and different letters representing different digits. What is $\overline{\mathrm{NINE}}=$ $\qquad$
$$
\begin{array}{r}
O N E \\
T W O \\
+\quad S I X \\
\hline N I N E
\end{array}
$$
【Analysis】First, find the special cases in the problem, the first letter in the result can only be the number 2, then look at the unit digit satisfying $O+X=10$, and the tens place satisfying $W+I=9$, enumeration can exclude the rest.

【Solution】According to the problem:
First, analyze that the numbers are from 2 to 9, so the maximum carry of three different numbers added together is 2, thus $N=2$; then, based on the unit digit being $E$, we have $O+X=10$. This carries 1 forward, and then we get $W+I=9$; the pairs of numbers that sum to 9 are $3+6$ or $4+5$. The pairs of numbers that sum to 10 are $3+7$ or $4+6$. Since 4 and 6 are repeated, the pair that sums to 10 must be $3+7$. When $O=3$, the number for $I$ is 4 or 5, and $T+S$ must result in 20 or 21, which has no satisfying numbers. When $O=7$, the number for $I$ is 4 or 5, and $T+S$ must result in 16 or 17. Then, $9+8$ satisfies the condition.

The remaining number is $E=6$.

Therefore, the answer is: 2526.