Partial answer / possible strategy.
Let's say we have a solutions.
Just by interchanging c with f we get an other solution.
The same goes if we change b and e or a and d.
This means that the total number of solutions is a multiple of $2 \times 2 \times 2 = 8$
now finding the solutions:
A place to start would be to group 1 and 0 to form 10 and look for combinations in the numbers 2 to 10 (9 numbers) in such a way that 2 numbers add up to a third one. So we don't get any carry over except in the hundreds place.
This way we get at least 2 solutions (without interchanging digits between numbers) for a combination because since there is no carry over we can switch the tenths with the units (inside both the numbers in the addition)
Such a solutions would be:
$5 + 4 = 9$, $2+6 = 8$ and $7+3 = 10$
So we get the solutions:
$725 + 364 = 1089$ and $752 + 346 = 1098$.
based on the logic above we now have $2 \times 8 = 16$ solutions.
An other combination would be:
$3+5 = 8$, $7+2 = 9$ and $4+6 = 10$.
So we get the solutions:
$473 + 625 = 1098$ and $437 + 652 = 1089$ and the additional solutions obtained from interchanging values (16 in total).
So now we have at least $16 + 16 = 32$ solutions.
Next step.
g is clearly 1 since we can get a carry over of max 1 from the hundreds place.
So we are left with the digits 0 and 2 to 9 (9 digits) to group them in such a way that at least 2 of them (but not just the ones we place in the hundreds place) add up over 10 so we get a carry over so we can get different solutions from the case above.
One possible way of doing so:
$9+4 = 13$ (units place), $6+8 = 14$ (tenths place and we get a carry over from the units place so we end up with 15) and $7+2 = 9$ (on the hundreds place and we get the carry over from the tenths to reach 10).
The solutions is:
$769 + 284 = 1053$ and by interchanging the digits we get 8 solutions in total. Now we have 40.
This can go on until we find all possible combinations.
Indeed using a computer (sorry for that, but I got tired of blindly stabbing for solutions) you get 96 total solutions. Which matches my finding that the total number is a multiple of 8.