Two is probably one of the easiest player counts. Probably not as easy as four, but certainly easier than one, three, or five. I don't really know how it compares to 6 or more. I've only been through that horror once.
Well, you can successfully run a session with only two players, only you will most likely lose. For me, it is not a big issue losing on this game, after all you are going to be in this situation a lot. But I agree that the best solution is for each player to control two characters, because this way you can stretch your turn a little bit more so it'll give you more options to think and you will grasp the little things quicker.
If you want walkthroughs, there are a few that you can go. Rahdo's is very clear:
There is one that it is pretty good, but it's a Brazilian guy, so it'll be unlikely that it'll be useful for you.
But bear in mind that this is not a very hard game to learn, just hard to master, so go on with two players and four characters, prepare for the likely event of losing, and have fun.
I find the game easier to win with 4 than with 2 if the team is composed to work well together.
EH scales the clue tokens, gates, monsters, and so forth well for the number of investigators. However, it missed two critical areas for scaling: first, moving to cover the board; and second, rate of mythos card draws.
The problem you will have with 1-2 investigators involves mythos cards popping up across the board from the investigators. With 4 investigators you will most likely have 1 within 0-2 moves of the event, while with 1-2 you will probably have 1-3 moves to get there. That loss of an entire turn moving could be disastrous.
The other issue is with the increased frequency of card draws. Yes, they are scaled down, but there are still issues. Getting 2 total actions, a rumor card, 2 more actions, and a rumor card again may be far more devastating than 4 actions, a rumor card, 4 actions, and a rumor card even though you need more clues to solve them.
I have not yet thought of a good solution for balancing as of yet, but I haven't been playing a lot of EH lately. I love it, but I've had a recent influx of games I have been playing while not having a lot of time to play. If I ever get to playtest anything, I'll post it under variants.
Two players should be ready to solve the first rumors if necessary, by grabbing and early clue, making sure they are well stocked on tickets to travel as far as they can in one turn. If they are prepared to knock out the rumor cards within a few turns of them appearing, they are good to go.
The "trap" is to focus on the first mystery so hard that you are unprepared for the first two rumors. You aren't under any time crunch to finish the first mystery, but you are under a crunch to finish the rumors, so do them first.