.exe translates to
dot e-x-e. In writing, however, should one say an .exe or a .exe?
In formal technical writing, normally it is written for example
The directory contains a .exe file
because you are typing the shorthand for dot-exe.
However, you could write:
The directory contains an exe file.
However, this does NOT feel good, and IMHO, I would say that it is probably better to write:
The directory contains an executable (.exe) file
I have proof read documentation for a number of large US software companies for many long years, and that is what their guidelines (or accepted common practices) were.
I hope that helps.
P.S. I personally would not say that this is a duplicate question, as it pertains more to formal technical writing, than common day narrative. The forms can vary somewhat. :-)