VTEC-E (for "Efficiency") is a form of VTEC that closes off one intake valve at low RPMs to give good economy at low power levels, while "VTEC" is a mode that allows for greater power at high RPMs, while giving relatively efficient performance at "normal" operating speeds.
"Three-stage VTEC" gives both types in one engine, at the cost of greater complexity and expense.
This works similarly to the principle which gave the Buick "Nailhead" V8 its reputation for high torque (in that case, the engine had notably small intake valves, giving good torque, but limiting peak power).
In an engine running at lower RPMs, a smaller intake valve area forces a given volume of air to flow into the chamber faster; this causes the fuel to atomize better, and therefore burn far more efficiently.
From ~5200 RPM to the rev limiter, the engine's high-lift VTEC cam lobe is engaged.