E/F# gives the bass its own instruction: keep the upper chord, but make the lowest note. The slash separates those two jobs.
F# is not in the upper triad; it supplies the upper chord’s ninth from below. Hold the upper chord steady and move only the bass. That low line can connect nearby chords without jumping root to root.
Also written E over F# or E with F# in the bass.

In which keys. Every note of E/F# belongs to C# minor (the ♭III), E major (the I), F# minor (the ♭VII), Ab minor (the ♭VI), A major (the V) and B major (the IV).
Read E/F# as a sus chord, written another way.
Contains E/F# and adds sixth.
Contains E/F# and adds fourth, sixth and major seventh.
Contains E/F# and adds sharp eleventh, sixth and major seventh.
Adds fourth, sixth and flat seventh. The flat seventh pushes the sound toward a dominant chord.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.