It can be played solo: my first several games were. You'll end up with most if not all of your games going to the final fight with the Ancient One (though wins by sealing or closing gates are possible, with enough practice, not that I've ever managed), but some of those fights are reasonably winnable. Running two investigators solo is easily manageable (some people run up to four, but that would be too many for me), and while it's not quite as fun (in my opinion) as a game with two players taking one investigator each, it's still good fun.
The only bit you miss out on playing that way is discussions/arguments between players about the best course of action (and you also don't have someone who might spot that you forgot to move the monsters this mythos phase, or some other silly mistake) but that's bearable.
Another advantage of playing with just one investigator: it'll be quite a while before you get to the stage of needing any expansions to increase the difficulty because you're winning too often.