10. (10 points) Football teams $A, B, C, D, E$ are in a round-robin tournament (each pair of teams plays one match). In each match, the winning team gets 3 points, the losing team gets 0 points, and in case of a draw, both teams get 1 point. If the total points for teams $A, B, C, D$ are $1, 4, 7, 8$, respectively, please answer: What is the maximum number of points that team $E$ can get? What is the minimum number of points that team $E$ can get?
【Analysis】In a single round-robin football match, there are a total of $4+3+2+1=10$ games. From the scoring criteria, a win or loss in a match earns 3 points, while a draw earns a total of 2 points. The question asks for the maximum and minimum scores of Team $E$, which clearly depends on the number of draws in the entire competition. The fewer the draws, the higher the score for Team $E$; the more the draws, the lower the score for Team $E$. Assuming all games earn 3 points, 10 games would total 30 points, with each draw reducing the total score by 1 point.

From the scores of $A$, $B$, $C$, and $D$, it is not difficult to analyze:
$$
\begin{array}{l}
A=1=1+0+0+0 \\
B=4=3+1+0+0=1+1+1+1 \\
C=7=3+3+1+0 \\
D=8=3+3+1+1
\end{array}
$$

From the scores, there are at least 3 draws, and the total score for all games is $30-3=27$ (points). The maximum score for Team $E$ is $27-1-4-7$
$$
-8=7 \text { (points). }
$$

From the scores, there are at most 5 draws, and the total score for all games is $30-5=25$ (points). The minimum score for Team $E$ is $25-1-4-7$
$$
-8=5 \text { (points). }
$$

Answer: Team $E$ can score at most 7 points and at least 5 points.