689 and 986 First, we see that the smaller number has to be from 599 to 702, because the sum of the digits of it has to be 23 and it must be less than 1000-297. Also, when you add 297 to the smaller number, the hundreds digit becomes 3 more and the units digit becomes 3 less. This means that the smaller number has units digit 3 more than hundreds digit. The only option from 599 to 702 that works is 689. So 689 and 986 are the 2 numbers.

not that bad of a problem if you write some equations call the two three digit numbers h1 t1 h2 and h2 t2 h1 we are given that the difference between these two numbers are 298 now we break this into two cases case 1: h2 - h1 = 7 bashing we end up with the two pairs $(1,8)$ and $(2,9)$ using the second equation($h2$ + $t2$ + $h1$ = $23$) we find no one digit intiger solution is possible so we go onto case 2: case 2: (10 + h2) - h1 = 7 by bashing out a few cases we get the following: $(1,4)$, $(2,5)$, ($3,6)$, $(4,7)$, $(5, 8)$ and $(6, 9)$ only the last pair works by solving the equation we see that $t2$ is equal to $8$ by subtraction we see that the two numbers are $986$ and $689$ sorry my latex is so poor