On a closed track, clockwise, there are five boxes $A, B, C, D$ and $E$, and the length of the track section between boxes $A$ and $B$ is $1$ km, between $B$ and $C$ - $5$ km, between $C$ and $D$ - $2$ km, between $D$ and $E$ - $10$ km, and between $E$ and $A$ - $3$ km. On the track, they drive in a clockwise direction, the race always begins and ends in the box. What box did you start from if the length of the race was exactly $1998$ km?
1. First, calculate the total length of one complete revolution around the track. The distances between the boxes are given as follows:
   - From $A$ to $B$: $1$ km
   - From $B$ to $C$: $5$ km
   - From $C$ to $D$: $2$ km
   - From $D$ to $E$: $10$ km
   - From $E$ to $A$: $3$ km

   Therefore, the total length of one complete revolution is:
   \[
   1 + 5 + 2 + 10 + 3 = 21 \text{ km}
   \]

2. Next, determine how many complete revolutions are made in a $1998$ km race. This can be found by dividing $1998$ by $21$ and finding the remainder:
   \[
   1998 \div 21 = 95 \text{ remainder } 3
   \]
   This means that after $95$ complete revolutions, there is an additional $3$ km to be traveled.

3. Now, identify the starting box by considering the additional $3$ km. We need to find the box where, if we travel $3$ km clockwise, we land on a box. Starting from each box:
   - From $A$: $1$ km to $B$, $5$ km to $C$ (total $6$ km), $2$ km to $D$ (total $8$ km), $10$ km to $E$ (total $18$ km), $3$ km to $A$ (total $21$ km)
   - From $B$: $5$ km to $C$, $2$ km to $D$ (total $7$ km), $10$ km to $E$ (total $17$ km), $3$ km to $A$ (total $20$ km), $1$ km to $B$ (total $21$ km)
   - From $C$: $2$ km to $D$, $10$ km to $E$ (total $12$ km), $3$ km to $A$ (total $15$ km), $1$ km to $B$ (total $16$ km), $5$ km to $C$ (total $21$ km)
   - From $D$: $10$ km to $E$, $3$ km to $A$ (total $13$ km), $1$ km to $B$ (total $14$ km), $5$ km to $C$ (total $19$ km), $2$ km to $D$ (total $21$ km)
   - From $E$: $3$ km to $A$, $1$ km to $B$ (total $4$ km), $5$ km to $C$ (total $9$ km), $2$ km to $D$ (total $11$ km), $10$ km to $E$ (total $21$ km)

   We see that starting from $E$ and traveling $3$ km clockwise lands us at $A$.

Conclusion:
\[
\boxed{E}
\]