The answer is $\boxed{\text{E}}$.

The sequence is generated by the following rule:

  • Start with the numbers $4$ and $7$.
  • Add $3$ to each number to get the next number in the sequence.
  • If the sum is greater than $20$, subtract $14$ from it to get the next number in the sequence.

Therefore, the next two numbers in the sequence are $19$ and $14$.

Here is a table showing the first few numbers in the sequence:

Number | Rule | Result ------- | -------- | -------- $4$ | Start with $4$ | $4$ $7$ | Add $3$ to $4$ | $7$ $10$ | Add $3$ to $7$ | $10$ $13$ | Add $3$ to $10$ | $13$ $20$ | Add $3$ to $13$ | $20$ $16$ | Subtract $14$ from $20$ | $16$ $19$ | Add $3$ to $16$ | $19$ $14$ | Subtract $14$ from $19$ | $14$

I hope this explanation is helpful!