I am a piano player of 15 yrs., and I've self taught myself from day 1 until last year. I must say that I was able to successfully learn some famous works, such as Clair de Lune (Debussy), Liebestraum (Liszt), To Spring (Grieg), 6 Poems after Heine (MacDowell), Moonlight Sonata and Sonata Pathetique (Beethoven), and more by the age of 12 (that's 7 years of playing.) Comparatively, a friend of mine took beginning piano lessons for a year and learned Clair de Lune, playing it much better than I initially did (technically speaking.) However, he could not perform it as musically as I could.
To learn something most efficiently, I recommend lessons, as the teacher can guide your technical skills best. I decided to get lessons when I was 19 (last year), and I drammatically improved in my abilities to read and perform pieces which were deemed impossible by my technical experience to play. (In example, I mastered Chopin's Revolutionary Etude in two months, whereas the most difficult piece I could play decently before that was Grieg's To Spring.)
After taking lessons, my technique became refined and my site reading skills dramatically improved. AND: my musical horizons were expanded. I learned several new artists, composers, and styles that I was previously unaquainted with (ie. Rachmaninoff, Barber, Vladmir Horowitz, Jazz).
However, self-teaching taught me something valuable: memorization and playing by ear. I've developed an uncanny ability to memorize a piece, whatever length, in a maximum of three days. Within a week I would have sufficiently mastered it, and within two weeks, improved it enough to perform. What is more, I will never forget what I've learned. Unfortunately, as a teacher, I have no idea how to teach my students how to memorize. I personally don't know how I do it, therefore can't teach them.
The other benefit is playing by ear. I find it very easy to pick up a piece from the radio and play it fairly close to what it sounds like. I don't know whether teachers can teach that to students, for my instructor doesn't need to teach me that.
To answer your original question: "Is there another way to do this?" Yes. Play the piano as much as you can. Pick up new music all the time. Read as much as you can, and, more importantly, listen to as much music from that genre as you can. That is my answer.
If you do decide on piano lessons, make sure you learn by intervalic teaching style, as opposed to middle C and the third style (whatever it is.) It is the easiest, most practical, and most efficient, as what you play after learning the basics is entirely based off that technique.
I hope this has been helpful!