10. (15 points) The sum of ten different non-zero natural numbers is 102. What is the maximum value of the sum of the two largest numbers? What is the minimum value of the sum of the two smallest numbers?

保留源文本的换行和格式，翻译结果如下：

10. (15 points) The sum of ten different non-zero natural numbers is 102. What is the maximum value of the sum of the two largest numbers? What is the minimum value of the sum of the two smallest numbers?
10. (15 points) The sum of ten different non-zero natural numbers is 102. What is the maximum value of the sum of the two largest numbers? What is the minimum value of the sum of the two smallest numbers?
【Analysis】The sum of ten different non-zero natural numbers is 102. When the sum of the two largest numbers is at its maximum, the other 8 numbers should be the smallest 8 different non-zero natural numbers, which are $1,2,3,4,5,6,7,8$. Solve accordingly.
【Solution】Solution: The maximum value of the sum of the two largest numbers is:
$$
\begin{array}{l}
102-(1+2+3+4+5+6+7+8), \\
=102-36 \\
=66
\end{array}
$$

The minimum value of the sum of the two smallest numbers is:
$$
1+2=3 \text {. }
$$

Answer: The maximum value of the sum of the two largest numbers is 66, and the minimum value of the sum of the two smallest numbers is 3.