jmc

Let the two three-digit numbers be $\overline{abc}$ and $\overline{def}$. Their sum is equal to $100(a+d)+10(b+e)+(c+f)$. To minimize this, we need to minimize the contribution of the $100$ factor, so we let $a=4$ and $d=5$. Similarly, we let $b=6$, $e=7$, and then $c=8$ and $f=9$. The sum is $$100(9)+10(13)+(17)=1047\to \boxed{1047}$$