Three. (25 points) It is known that there is a four-digit number, and the sum of this four-digit number and the sum of its digits is 2004. Find this four-digit number and explain your reasoning.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
Three, let this four-digit number be $\overline{a b c d}$. From the problem, we get
$$
1000 a+100 b+10 c+d+a+b+c+d=2004 \text {, }
$$

which simplifies to $1001 a+101 b+11 c+2 d=2004$.
Clearly, $a=1$ or 2, otherwise $1001 a>3000$.
(1) When $a=1$, subtract 1001 from both sides of equation (1), we get
$$
101 b+11 c+2 d=1003 \text {. }
$$

Since the maximum value of $11 c+2 d$ is $99+18=117$, hence $101 b \geqslant 886$, so $b=9$. Thus, we have
$$
11 c+2 d=1003-909=94 \text {. }
$$

Since $0 \leqslant 2 d \leqslant 18$, it follows that $94-18 \leqslant 11 c \leqslant 94$.
Therefore, $c=7$ or 8.
When $c=7$, $11 c+2 d=77+2 d=94$, we get $d=\frac{17}{2}$ (discard);
When $c=8$, $11 c+2 d=88+2 d=94$, we get $d=3$.
In this case, the four-digit number is 1983.
(2) When $a=2$, subtract 2002 from both sides of equation (1), we get
$$
101 b+11 c+2 d=2 \text {. }
$$

Therefore, $b=0, c=0$.
Hence, $d=1$.
In this case, the four-digit number is 2001.
In summary, the four-digit numbers sought are 1983 and 2001.