We need to find the lowest common multiple of 10, 12, 16, and 18, which is 720.
To find the remainder when 2000 is divided by 720, we can use long division or modular arithmetic:
$$
\begin{array}cc
720 & 2000 & \\
\hline
& 2\cdot720 & (1440) \\
& 280 & \\
\hline
& 200 &
\end{array}
$$
So the remainder when 2000 is divided by 720 is 200.
To make the sum divisible by 720, we need to add the difference between 720 and the remainder (520):
$$
2000 + 520 = 2520
$$
Therefore, the lowest number that must be added to 2000 so that the sum is divisible exactly by 10, 12, 16, and 18 is 520.