This passage is talking about God's final judgment at the end of the world. If you look at this passage it looks like God will judge you based on your actions and reward according to your works. However, Paul builds the case for Jesus throughout the entire book of Romans. And how we need to be saved by grace and faith in Him along. If we understand that, then verses appear to contract the theme of the book of Romans. However, we know that scripture does not oppose it's self, therefore we view these verses in light of what Paul is saying overall.
This passage, in context of the entire expose to the Romans, Paul maintains that we are saved by grace ( Romans 3:23-24 ), that no one will be declared righteous by observing the law ( Romans 3:19-20 ) and finally, that we will only be justified through faith in what Jesus did for us. ( Romans 3:24-28 ). Therefore, the only action that will be rewarded with eternal life is the action of faith not of works.
We have a choice in this life. The choice we have in this life is the choice of faith in Jesus. Faith is what saves us, not individual good works. We must put our faith in Jesus and that alone is the only thing that God will judge in determining eternal life verses wrath and anger.
What Paul is describing is that faith is an action. James says, that true faith has actions. "In the same way, faith by itself, if it is not accompanied by action, is dead. But someone will say, "You have faith; I have deeds." Show me your faith without deeds, and I will show you my faith by what I do." ( James 2:17-18 ). Paul is attesting to this, He is saying that for those whose faith is so real, it causes them to continue to do well... 'seeking glory, honor and immortality'... the result is eternal life. On the other hand, for those who reject the truth, the truth of what Jesus did for them, and follow in the ways of the world, then there will be destruction. It all boils down to a choice and the corresponding actions associated with believing that choice.
Today, it is my prayer that as you make this choice to trust Jesus with your life, you will continue on into the fullness of Christ. By knowing Him, the choices you make in life will spur you onto good deeds out flowing from His goodness and love. Paul says, the result is eternal life with our Lord and Savior! Amen!