Example 14. There are 10 pieces of paper, on each of which the positive integers from 1 to 10 are written. Then they are all folded and placed in a hat. Five people are then asked to each draw two pieces of paper (the pieces drawn by each person are not returned to the hat). Unfortunately, an error occurred in recording the results. At this point, the person in charge proposed a method, asking the five people to each state the sum of the numbers on the two pieces of paper they drew: $A[11], B[4], C$ [7], $D[6], E[17]$. How can we determine which two numbers each person drew?
(1) From $B=4 \Rightarrow B=1+3$,
(2) $C=7=\left\{\begin{array}{l}1+6, \\ 2+5, \\ 3+4,\end{array}\right.$

but 1, 3 are already determined, $\therefore C=2+5$;
(3) From $A=11=\left\{\begin{array}{l}4+7, \\ 3+8, \\ 2+9, \\ 1+10,\end{array}\right.$

and 1, 2, 3, 5 are already determined,
$$
\therefore A=4+7 \text {, }
$$
(4) From $D=16=\left\{\begin{array}{r}10+6 \\ 9+7\end{array}\right.$,
and 7 is already determined, $\therefore D=10+6$,
(5) From $E=17 \Rightarrow E=8+9$.