Mainly, it's going to be string height and/or the angle at which the string vibrates.
If you change string gauges, you will most definitely get string buzz. That's strictly based on the fact that a heavier gauge string (or set of strings) adds more tension on the whole construction of the guitar. To a certain extent, the neck of the guitar is flexible. The same thing happens when you detune a string, as the neck will be "pulling" itself back, thus slightly reducing string height.
On electric and acoustic guitars the neck will almost always contain 1-2 truss rods. The way these work is that they internally tighten the neck so as to compensate (and almost match) the tensions with which the strings are pulling.
You need to slowly and slightly adjust the truss rod, retune the whole guitar, allow to sit for a bit of time, and test again. You need to allow the wood to settle before adjusting again. Your best bet is to only adjust by turning it no more than a quarter of a turn at a time. Keep in mind that the neck is supposed to have a slight bow.
Moving on, there are other factors which will contribute to fret buzz, too. On your particular type of guitar, the bridge has two height screws for each string. Technically, you want to adjust them so that the strings are level. Adjusting those two screws independently will also permit the string to vibrate at an angle, too. Keep in mind that strings don't only vibrate on a single axis.
The odds of having issues with the depth of the slot for the E string are rather low, I would say. Be aware of the fact that nut slots have different depths and widths, based on the string gauge. The slot for a low E will be wider than the one for the high E - and that's perfectly normal. More depth is needed so that the string doesn't simply fall off the nut when you're playing.
Of course, what I've mentioned here is just theory. I suggest, like many others have, to search for tutorials on how to properly adjust your type of guitar. By "type", I don't necessarily mean the specific model of guitar, but the type of truss rod configuration (I presume yours only has one, with adjustment access on the headstock, behind the little plastic triangle with "H-1001" written on it) and bridge type.
Whilst you're at it, I'd also recommend adjusting intonation, too. That involves adjusting string length in order for notes to be perfectly in tune regardless of the fret.
A few things you might want to know before proceeding:
- Adjusting your truss rod is somewhat dangerous. If you overtighten it, you can snap the neck.
- Adjusting the truss rod with the wrong tool is going to be bad, too. Make sure you're using the appropriate metric/imperial allen keys. The small difference between very similar metric/imperial key sizes will wear out the bolt, and you'll almost never going to be able to adjust it again.
- Make sure to not adjust the rod more than it can go. On certain guitars, it's hard to feel.
- Be prepared for this to take a full day if it's the first time you attempt it.