Both Roman Catholics and Eastern Orthodox believe that works are part of the requirement for salvation.
Ahhh, I notice how you slipped in "part of...". Are there no RC's on this thread? Every time I've heard a RC told that he/she believes that salvation is through works and not a gift of God, the RC has strongly protested and disagreed. If you don't mind, I'll wait for a RC to tell me what he/she believes. And the question, still stands - any Christian on this thread believe that salvation is through works?
That is an oft quoted misunderstanding.
What is practiced in the RC and EO churches can be captured in: "Faith without works is dead:(James 2:20)".
Example:
One can claim to have faith in God. Along with that, one can fervently believe that the Apocolypse is nigh, that going to Church every Sunday is the trump card to get you into heaven, and that when you see your fellow congregation members in the liquor store, they're saved because they have 'faith'.
It means squat. The only evidence that a person truly has faith in God is evidenced in their works ( actions ), no matter how loud they hosanna or beat their Bible. And that is where faith and works applies. A man is justified by faith but only if it is true, and through that faith it will manifest in the way he conducts himself.
The misunderstanding of your quote above is rooted in a time in the Catholic church in which that doctrine truly did carry some weight ( like indulgences in exchange for merely a substantial donation to the Church coffers, or salvation merely for going to war at the behest of the local Bishop ). However, despite that period, the consistent doctrine is as I stated above.