7. (10 points) Five contestants $A, B, C, D, E$ participate in the "The Voice" competition, and the five of them stand in a row for a group appearance. They each have a contestant number on their chest, and the sum of the five numbers is 35. It is known that the sum of the numbers of the contestants standing to the right of $E$ is 13; the sum of the numbers of the contestants standing to the right of $D$ is 31; the sum of the numbers of the contestants standing to the right of $A$ is 21; the sum of the numbers of the contestants standing to the right of $C$ is 7. What is the sum of the numbers of the contestants standing at the far left and the far right? $\qquad$


【Analysis】According to the problem, among the five participants, $A, C, D, E$ all have someone to their right, so the person on the far right is participant $B$, and $B$'s number is 7. The order of the five participants can be deduced from this, and the final sum can be calculated.

【Solution】Solution: According to the analysis, among the five participants, $A, C, D, E$ all have someone to their right, so the person on the far right is participant $B$, and $B$'s number is 7;
The sum of the numbers of the participants to the right of $E$ is 13, so to the right of $E$ are $C$ and $B$, and $C$'s number is: $13-7=6$; The sum of the numbers of the participants to the right of $A$ is 21, so to the right of $A$ are $E, C, B$, and $E$'s number is: $21-13=8$; The sum of the numbers of the participants to the right of $D$ is 31, so to the right of $D$ are $A, E, C, B$, and $A$'s number is: $31-21=10$; The remaining number for $D$ is: $25-31=4$, so the participant on the far left is $D$, and the sum of the numbers of the participants on the far left and far right $=4+7=11$.

Therefore, the answer is: 11.