The "E" stands for an "economy" behaviour of the gear-shifting where the auto box always starts with gear-2 and works its way up as you accelerate. In this mode, gear-1 is never started with unless you absolutely and sharply floor-the-pedal. Also, takeoffs will be smooth, and comfy with only the needed fuel going to the engine thus yielding frugal performance (economy).
The "S" stands for "standard" or "sports" modes as I've been seeing in different manuals (must be a regional thing). In this mode, takeoffs in gear-2 occur only if the pedal is pressed lightly, otherwise normal pressing/pedal pressure triggers off selection of gear-1 for takeoff though a change to gear-2 follows almost immediately. Stabbing the pedal without letting back too much on the other hand tells the car to hold on to gear-1 for as long as your foot doesn't ease back...up to the point where the gearbox decides to shift up. This yields sporty, sharp responsive performance, good acceleration for the given engine.