Something like this should work. We'll use capture groups (\(\)) and back-references (\1,\2) to do the swap, and the right pattern to find all the right places.
This one I wrote from scratch, but if I wasn't sure to get it right I would first search interactively (or using :global) until I got the right pattern, then use :%substitute//... to re-use the pattern.
%substitute/\\operation{\(e_[^}]*\)}{\([^}]*\)}/\\operation{\2}{\1}
Add /g if you have more than one on a line.
We use [^}]* to simulate a non-greedy .* (vim can do this with .\{-}), but in this case we really only want until the next }. If A and B can contain nested {}, which is generally true in LaTeX, you might have better luck with .* or .\{-}, or you might need something far more sophisticated. An example:
global/\\operation{e_/normal! 0f{di{;vi{p%,p
Breakdown:
:global/\\operation{e_/: for every line matching the pattern:normal!: do these normal mode key-strokes without mappings0f{di{: delete the first argument;vi{p: paste it over the second%,p: paste the second argument back in the first spot
This will handle {} oddities more readily, since we let vim do the complex nested-matching for us (regular expressions aren't powerful enough).
Realistically, I would record a macro (probably with trial and error):
qq0f{di{;vi{p%,pq
and then do
global/\\operation{e_/normal! @q
