Wow, I have to admit that one sorta took me by surprise! But, this passage of Romans 2reveals a very important point about the the group that is to receive immortality: Verse 7 says they are engaged in "well doing" and verse 10 says they "worketh good". However, only those who have been previously saved are capable of doing well and of good work...
There are many good works, even the evil ones can do good to those they love, even atheists can give to the poor, house the homeless, etc.,...but here is the difference (the clue) these were "doing well" in an attempt to obtain immortality (eternal life), but it cannot be obtained by doing good works...the good works that count are those produced by the Spirit in the children of faith (Ephesians 2:10) who already have it...
We are not saved by ourselves nor by any works of righteousness that we do...we are saved by grace through faith. But if we are saved (have already "eternal life" which does not ever cease as opposed to eternal death which is conscious separation from God and all He would provide forever) we will produce much fruit (Matthew 25) for the kingdom....
"Eternal life" does not speak to continuous existence alone, it is sharing in God's life, being a child of God (a real eternal spirit being with a glorified body, Him really being our ABBA our Dad). Even those who are in hell will endure continued conscious existence (the second death) but ever without order to cool the fires of chaos, ever without touch, or fellowship with even one other, all their soulish desires burning but never even a drop of water...and all because the rejected God and did not believe God....