No one is saying that there isn't an obedience that comes by faith.
We are saying that salvation itself is through faith alone and not of works.
Ephesians 2:10 is not going to contradict the previous two verses; which tell us that salvation is not of works.
So then, the works that we do that God has prepared for us to do, do not save us (Ephesians 2:9); but they stem out of a salvation that is already given.
Regeneration and renewing of the Holy Ghost (Titus 3:5 (kjv)) is going to have the effect of changing a man's heart so that he walks according to love.
But I want to say to you that apart from that regeneration, no amount of attempting to walk by love is going to produce that love in a person's heart. That love only comes in through faith in Jesus Christ (Galatians 3:14, Romans 5:5).
Again, if I give $5 to the poor, or even $5,000,000, that is not going to produce a change in my heart so that I have actual love in my heart (salvation). I can indeed give to the poor from motives not of the love of Christ. I may want the acclaim. I may think that I am earning my position in heaven. But the only motivation that counts is love for the Lord over the fact that He has already redeemed you from a horrible fate (hell and the lake of fire). You are not going to deliver yourself from that fate by doing good works.
It is only by a simple faith in Jesus Christ and His shed blood that you can be redeemed (Mary's blood was not shed on a Cross for you). If a man is truly redeemed, he will most assuredly love the Lord. And that love will not be in word or in tongue only, but in deed and in truth (1 John 3:17-18). It is also the fulfilling of the righteousness of the law within a man (Romans 13:8-10, Galatians 5:14, 1 John 5:3, 2 John 1:6, Romans 8:4).
But this love comes in as the free gift of the Lord to a man's soul; through faith alone in Jesus Christ alone (so, putting your faith in your works to save you is going to detract from faith in the One you must surely put your faith in to be saved).
God gives us the gift of righteousness (Romans 5:17) as a free gift (Romans 5:15-19, Romans 6:23).
Again, the faith that apprehends this righteousness does not have works included therein. But it does produce works as a separate result. And the works don't save you in the slightest (Romans 4:5-6, Titus 3:5 (kjv), Ephesians 2:8-9).
Tit 3:5, Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;