How can I best convert .jpe images to .jpeg format?
You can certainly convert JPE images directly to JPEG images (.jpe to .jpeg conversion), it would, however be quite pointless, since both file types are essentially JPEG Images using different suffixes.
If really needed, simply rename your file's JPE suffix to JPEG.
Regardless of that, you can obviously use numerous available graphics editing programs or (online) conversion tools capable of converting JPE to JPEG.
A bitmap graphics editing program
Raster graphics and 3D computer graphics application, which is a refresh of Microsoft Paint.
A complete image retouching program
A popular utility for viewing and converting graphic files