This suggests that Luther resolved in a unique way what I have previously referred to here as the "Augustinian dilemma." Augustine taught two very difficult to coordinate things: 1. In the anti-Donatist writings he taught that the visible Church and the means of grace absolutely guaranteed the presence of divine grace. 2. In the anti-Pelagian writings, he taught that salvation depended on the divine act of predestination and that everyone who received the means of grace aren't necessarily saved. The tension is created by the fact that the presence of grace in the visible Church doesn't necessarily translate into the guarantee of salvation. It brings about the question of how in light of predestination we really know if God is on our side. Since then the west has split up on this basis. On the one hand, the Reformed took Augustine's doctrine of grace at the expense of his doctrine of the Church, whereas the Catholics took his doctrine of Church at the expense of his doctrine of grace. Obviously this isn't true for every theologian (Jansen and Thomas Aquinas are hardcore predestinatarians) but it's generally the case.
Part of this also relates to Augustine's view of Christology. Like Leo after him, Augustine definitely emphasized the distinction between the two natures. This translates into his doctrine of the Church and the sacraments. Much as Christ's two natures are divided, so too are the visible and invisible Church, as well as the visible means of grace and God's invisible working of grace.
Both the Reformed and the Catholic Church buy into this in different ways. The Catholic Church holds that because the risen Christ isn't present everywhere or definitely tied to certain visible means, it's the Church's job to bring the gap. We can see this in the teaching office. Because the Word doesn't automatically authenticate itself by the presence of the risen Christ, the Pope brings the gap between Jesus in heaven and us on earth. The current pope puts it this way in some of his writings: when the ascension happened, the "head" of the totus christus was detached and so in order to replace it, Peter must exercise Christ own office until he comes. In the Lord's Supper, Jesus is in heaven, so how can he come down? He comes down because the priest is given certain powers by virtue of his ordination to bring him down. The Reformed follow this same logic and with the lack of a priest to draw him down from heaven, they are stuck with the assumption that it has to either be just a symbol or that we have to go up to him.
In both cases, the idea of grace becomes distorted. The Catholic assumes that redemption is a possibility offered in the presence of Christ in the visible Church. We then need to use our free will to tap into that possibility. For the Reformed, the visible means of grace actually tell us nothing. Faith is really a "sign" that one is elect. It is a correspondence to God's gracious decree, not trust that takes hold of God's tangibility in Word and sacrament.
This brings us to Luther. His breakthrough (which I would date around 1518-19, this is subject of another post) recognized that the Word "I absolve you" was identical with God's own gracious presence. This relates to what Martin Chemnitz would later call the "Genus Maiestaticum"- the claim that Christ possesses the fullness of divine glory according to his humanity. For Luther, just as the flesh of Christ the concrete manifestation of God and his gracious disposition towards humanity ("and there is no other God!" as the hymn states), so to the sacraments whereby God's gracious disposition towards us are made manifest are also the direct presence of God in, under, and with the elements.
This resolves the Augustinian dilemma in a highly paradoxical manner. How does one know that they are predestined? By receiving the Word. The Word itself is identical with God in Christ. To receive God is to know what God thinks of us. This means also that God's own predestinating act is identical with the event of coming to faith via Word and sacrament. Only existence apartment from and outside the sphere of the Word could make one uncertain of God's judgment in our favor. This accounts for the somewhat paradoxical description of God's action in predestination in Luther and the Formula of Concord. God in Word and sacrament makes it absolutely clear that he desires all to be saved. Nevertheless, for those who receive him in Word and sacrament, he gives an absolute guarantee that he will save them. In other words, this desire of all to be saved doesn't not merely exist as a possibility, but as an actuality for those who receive God's own being in the Word and sacrament. Nether is the offer limited. Because that is the case, then it must be an act of divine predestination. Otherwise, the person would have to have a measured faith in anticipation of whether one might fall away or not. But God in Christ has completely surrendered to us and given us absolute certainty. There is not other God lurking around, secretly wishing our demise. Hence, God not only desires all to be saved, but actually makes certain of those who come to faith that he has chosen them from eternity.