Here's a quote from Luther on this glorious truth reflecting on his conversion (and Romans 1:17):
"In it the righteousness of God is revealed," that had stood in my way. For I hated that word "righteousness of God," which, according to the use and custom of all the teachers, I had been taught to understand philosophically regarding the formal or active righteousness, as they call it, with which God is righteous and punishes the unrighteous sinner.
At last, by the mercy of God, meditating day and night, I gave heed to the context of the words, namely, "In it the righteousness of God is revealed, as it is written, 'He who through faith is righteous shall live.'" There I began to understand that the righteousness of God is that by which the righteous lives by a gift of God, namely by faith. And this is the meaning: the righteousness of God is revealed by the gospel, namely, the passive righteousness with which merciful God justifies us by faith, as it is written, "He who through faith is righteous shall live." Here I felt that I was altogether born again and had entered paradise itself through open gates.
The bit (in the Table Talk) about if teaching about the atonement was just about forgiveness of sins (in the last 5 minutes), then it's like we're forgiven as a past event and now got to be good to make it, got to justify ourselves was especially helpful. It helped me understand where the Mormon missionaries were coming from yesterday when I questioned a passage of the Book of Mormon that they gave me, where it talks about Christ's death removing the curse of the fall and making us free to choose good or bad, and us being on probation because of it. Yes - probation, basically they believe that God is going to see if we are good enough to make it! But you expect Mormons' to have a false gospel - how many 'protestants' have that heretical view? Rather a lot: that we have to be a 'Christ-follower' obeying Christ to be saved is very common, thanks to the neo-pietists and semi-pelagians that infest the English and American churches today.
Yes faith without works is dead - but the works are fruit - because we are saved we will do them. We don't have to prove our faith to God - he gave us it, he united us with Christ, clothed us in Christ's righteousness, he hid our shameful lives in Christ. We have to prove it to ourselves, of course, to give assurance - that we have the down payment of the Spirit, that we have been worked in by the one who will finish what he started, due to his faithfulness. Our good works assure ourselves that God is working in us, rather than assuring God that we are worthy of him. It's getting things the wrong way round - the wrong view of 'because we want to be saved, we will obey our Lord', rather than 'because we are saved, we will want to obey our Lord'.
Without Justification, we can have no assurance - thank God for this gift of his grace, that we get what we don't deserve: the righteousness of God. God looks at Christians and sees obedience "to the point of death, even death on a cross." - he sees Jesus' obedience, not our disobedience.