It is true that we don’t find the words faith alone (Sola Fide) in the Bible to support of the faith alone position.  The term Trinity is not found in the Bible either, but the truth of the Trinity is revealed. We are saved by faith alone as communicated in Ephesians 2. This faith is not alone. It produces a willingness to serve God.  God has prepared those works for you. 

Ephesians 2:8-10  

For by grace you have been saved through faith; and this is not of yourselves, it is the gift of God; 9 not a result of works, so that no one may boast. 10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand so that we would walk in them.

The only time faith alone is used in Scripture is in James 2:24. Roman Catholics use this verse to support their view of works and faith as being meritorious for salvation. 

James 2:24

24 You see that a person is justified by works and not by faith alone.

There is no contradiction between James and Paul. They both teach that works are as result of faith. Paying God lip service that you believe in Him doesn't save you. Even the demons believe in God, but are certainly not trusting in Him for salvation (James 2:19). 

James 2:14

What use is it, my brothers and sisters, if someone says he has faith, but he has no works? Can that faith save him?

Romans 3:28

28 For we maintain that a person is justified by faith apart from works of the Law.