Regex to validate subtract equations like "abc-b=ac"

I've stumbled upon a regex question.

How to validate a subtract equation like this?

A string subtract another string equals to whatever remains(all the terms are just plain strings, not sets. So ab and ba are different strings).

Pass

abc-b=ac
abcde-cd=abe
ab-a=b
abcde-a=bcde
abcde-cde=ab

Fail

abc-a=c
abcde-bd=ace
abc-cd=ab
abcde-a=cde
abc-abc=
abc-=abc

Here's what I tried and you may play around with it

https://regex101.com/r/lTWUCY/1/

Solution

Disclaimer: I see that some of the comments were deleted. So let me start by saying that, though short (in terms of code-golf), the following answer is not the most efficient in terms of steps involved. Though, looking at the nature of the question and its "puzzle" aspect, it will probably do fine. For a more efficient answer, I'd like to redirect you to this answer.

Here is my attempt:

^(.*)(.+)(.*)-\2=(?=.)\1\3$

See the online demo

^ - Start line anchor.
(.*) - A 1st capture group with 0+ non-newline characters right upto;
(.+) - A 2nd capture group with 1+ non-newline characters right upto;
(.*) - A 3rd capture group with 0+ non-newline characters right upto;
-\2= - An hyphen followed by a backreference to our 2nd capture group and a literal "=".
(?=.) - A positive lookahead to assert position is followed by at least a single character other than newline.
\1\3 - A backreference to what was captured in both the 1st and 3rd capture group.
$ - End line anchor.

EDIT:

I guess a bit more restrictive could be:

^([a-z]*)([a-z]+)((?1))-\2=(?=.)\1\3$