Example 2 Green Mountains and Clear Waters

After the summer vacation group tour, the teachers talked about their impressions of the tour. The Chinese teacher said: "Green mountains, clear waters, strong pines, and a thousand beautiful peaks." The foreign language teacher said: "Beautiful peaks, a thousand strong pines, clear waters, green mountains." The math teacher said: "864197532." The above three sentences form an addition equation:

Each Chinese character represents a number from 1 to 9, with the same character representing the same number and different characters representing different numbers. Find this equation.
Explanation: Observe the first digit of the addition equation (the first digit of an addition equation is usually the easiest to start with). From the equation, we know that the difference between "秀" and "青" is at least 8, which has reached the maximum possible limit. Therefore, "秀" must be 9, and "青" must be 1.

The digits 1 and 9 have been assigned. The remaining digits are from 2 to 8, and the difference between any two of these numbers is at most 6.

In the second digit of the addition equation, the difference between "峰" and "山" is at least 6, which has also reached the maximum possible limit. Therefore, "峰" must be 8, and "山" must be 2.

Similarly, we can sequentially determine the remaining digits, and finally, we get the equation:
$$
123456789 + 864197532 = 987654321.
$$

By verification, the result is completely correct.