The AKG K701 / K702 / Q701 need more current than the majority of headphones, for equivalent listening volumes. Thus they've developed a reputation of being hard to drive or picky about amplification, and needing a desktop amplifier. The part about needing a desktop amplifier is not really true, as it just depends on the characteristics of the amplifier, not how large it is or from where the power comes from. Plenty of portable or battery-power devices can do it justice.
Most people would say the E7 is a little bit underpowered from driving the Q701, but if you don't listen at a loud level or listen to music that's heavily dynamic range compressed (most releases these days, where loud parts are squished into all being the same amount of loud), then that's not an issue for you. If you're satisfied with the volume and don't hear any distortion, it's okay. You can do a little better, but the E7 is not bad.
For reference, the E7 can output a fairly clean 1.6V or so into the roughly 62 ohms of the Q701, for approximately 104 dB SPL peak volume from a sine wave...at least according to independent tests of the E7 and of the Q701. The E9 is a bit cleaner according to bench tests but not significantly so. The main real advantage would just be being able to crank up the volume louder.
The other "advantages" would be (1) the higher output level and big knob encouraging you to listen somewhere in the middle of the rotation, which may be louder than where you currently listen, and louder almost always is perceived as better, and (2) it being a desktop amp, so of course it's "supposed" to sound better, so you would be inclined to think it sounds better. Same goes for most desktop amps.
