The movie is here:

http://www.themoviedb.org/movie/512338 - Added on March 2018.

Appears to be an issue of "and" vs "&" in the search menu. Shouldn't one be equivalent to the other when using search?

@Johnny Jackhammer said:
Trying to add a movie but the IMDb ID is already taken AND the movie doesn't appear to exist on tmdb.org
A message appears declaring the IMDb ID is already taken AND there is no information on which movie has taken it.
The title of the movie I am trying to add is "Satan & Adam" with tt0086190 as the IMDb ID.
I don't see a way to search by IMDb ID on tmdb.org.
https://www.imdb.com/title/tt7445772/

I believe the first IMDB ID is not the correct one.
tt0086190
The link you posted has the correct ID.
tt7445772

Search Tips
Search by IDs
See here: https://www.themoviedb.org/bible/general#59f793929251413e93000013
Example with IMDB ID

https://www.themoviedb.org/redirect?external_source=imdb_id&external_id={searchTerms}   
https://www.themoviedb.org/redirect?external_source=imdb_id&external_id=tt7445772   
https://www.themoviedb.org/redirect?external_source=imdb_id&external_id=tt0086190    

Appears to be an issue of "and" vs "&" in the search menu.
Shouldn't one be equivalent to the other when using search?

Both forms of research worked.
Using "and" was more accurate.

https://www.themoviedb.org/search?query=Satan+and+Adam  
https://www.themoviedb.org/search?query=Satan+%26+Adam  
https://www.themoviedb.org/search?query=Satan+&+Adam   

Consider that in this search using Title, all Title variations are considered.
Those used in translations and also Alternative Titles.