I'm curious why the rated that one hard.
They say the maximum length of the input digit string is 10, so there are at most 9 places where an operator can be inserted. At each possible insertion point there are 4 possibilities: insert one of the 3 allowed operators or do not insert anything.
That's only 262144 possible expressions. Just brute force evaluating all of them, filtering out the ones that do not equal the target, and then filtering out those that violate the no leading zeros requirement should be fast enough even on a slow computer.
The other hard ones I've seen have all allowed inputs large enough that brute forcing would be way too slow, and so cleverness is required. E.g., that shortest path in a grid problem that was posted a comment or two above. My first thoughts on that one were to just generate all possible paths with the obstacles ignored, and then find the shortest path(s) that do not cross more than the number of obstacles we are allowed to eliminate.
But the grid can be up to 40x40. By 10x10 we're already up to 41044208702632496804 possible paths [1], so brute force is not an option.
[1] https://oeis.org/A007764