I tried this once, but then I kept spending all my free time online, so I haven't learn anything meaningful. So I guess I am not the right person to give advice, but my opinion is that it is realistic, if you persevere. I know two people who learned playing the piano this way; one of them plays really good, the other one has only memorized a song or two (but it sounds great anyway).

Do you have the piano? Do you have free time to practice at a reasonable time of the day (because your neighbors might be unhappy about hearing you practice in late night)? Buying a keyboard with headphones could be a solution.

I asked people to recommend me the best book for learning. Unfortunately, I don't have it here, and I don't remember what it was.

I found it more motivating to play using a metronome (so when I don't press the right key at the right moment, I consider it a failure and start again). Playing this way reminds me of Dance Dance Revolution, and generally feels like playing a computer game.

Do you know the musical theory? It actually makes sense from mathematical point of view, if you understand the somewhat crappy notation. Tone = frequency of vibration. The tones are a geometric progression, where 12 "halftones" = double the frequency. Note that there are 12 keys (both white and black) in an octave; there is a halftone between each two adjacent ones. The white keys correspond to lines and spaces in the music sheets; you reach the black keys via prefixes.

EDIT: This may be useful for the piano.