Difficulty reaching lower E to higher G in left hand on piano

You do not always have to take notation literally; particularly note durations. When there are multiple voices in the left hand, it is common for one note or chord in the lower register to be given a very long duration, while shorter notes are proscribed in a higher register - often an octave or further apart. See this example from Rachmaninoff's Prelude in C# Minor:

He even does it with both hands; holding the low C#'s in the second measure far into the third. Try holding those octaves whilst performing the eighth-note chords; you would need four hands!

It is more about the impression of those low notes sounding for that duration; which you can do by playing them a little louder, and holding the sustain pedal for the duration. That works only if the higher notes are not staccato, which prohibits pedal. In your case, pedal would work fine.

Another example, this one from Liszt's Reminiscences de Norma:

This is an arrangement of a pop song. Nobody bothers about the correct interpretation of such an arrangement. You can accompany with the sustain pedal. The left hand chords can be held as long you want, take care with the passing tones in the right hand (f# bar 2, f# and d bar 3 etc).

In a classical piece you have to be more correct.

But then you could apply a sostenuto pedal:

On a modern grand piano with three pedals, the middle pedal is usually a sostenuto pedal. It sustains only those notes that are being held down when the pedal is depressed, allowing future notes played to be unaffected. It is commonly abbreviated "S.P.", "Sost. Ped.", or "ThP." (from the German equivalent "Tonhalte-Pedal").

On some upright pianos and lower-quality grand pianos, the middle pedal sustains all notes in the bass register, but this is not a true sostenuto pedal. On other uprights, the middle pedal is a practice pedal (with a locking option), which makes the sound extremely quiet beyond the standard soft pedal. This is often achieved by dropping a felt cloth between the hammers and the strings when the practice pedal is depressed. Not all pianos have a sostenuto pedal, however. Some older, or modern low-quality uprights do not have this option.

https://en.wikipedia.org/wiki/Sostenuto