The Damned Brotherhood is by definition a militant order of the Adeptus Ministorum. During his initiation into the order, a Damned Brother proclaims himself lost to the warp for the sake of the Imperium. It is a young, and as yet unofficial group among the Adeptus Ministorum that draws heavily from reformed heretics. What seperates the Brotherhood from similar fanatical organizations is that the Damned Brotherhood believes that anything goes in the battle against the enemies of the Emperor. They have no problem using the weapons of the foul xenos against them, just like they will use the powers and tools of the Warp against chaos. They don't view this as having a pass to do what they will, however, a ritual of justification must be performed, it must be determined that the act is truly for the benefit of the Emperor and his subjects, rather than the benefit of the cleric. Beyond that, the Brotherhood punishes those who emulate their ways without understanding their methods most severely of all. The similarity in philosophy between the Damned Brotherhood and the Xanthite faction of the Inquisition has led some to speculate that the Radical faction might have had a hand in creating the Brotherhood.
Solon Modrak was not one of those reformed heretics, he joined the Damned Brotherhood in his youth, believing that his life was of less value than those he might save. He has served honorably since then. After a particularly noteworthy service involving protecting his flock from a cult of the Ruinous Powers, Solon was recruited into the service of Inquisition.
Except that none of that is true. There is no such thing as the Damned Brothrhood, except for Solon, and Modrak himself is as much fiction as the story of his order. Solon was born with, or at least, was previously known by the name Ingenuus, the child of hiver manifactorum workers. After his entire family was killed in an accidental explosion, Ingenuus turned from the Imperial Cult, managing to convince others to follow him and managed to shut down that entire sector in protest. He transformed from a provocator to a revolutionary when the local, underequipped regiment of Planetary Defense Force stepped in to restore order. Ingenuus and his subjects waited in ambush with wrenches, knives, screwdrivers and whatever else they could fashion into a weapon and slaughtered the guardsmen, improving their armaments in the process.
This went on for some time, long enough that the image of Ingenuus's scarred visage, chainsword in hand, became a common sight on posters throughout the hive, both expressing support and revulsion of his cause. Eventually, the Imperial Guard was called in, and Ingenuus's rebellion was crushed. The leader was taken alive, however, with the intention of torturing him until he begged forgiveness and then executing him as an example.
For whatever reason,an Inquisitor found reason to step in and recruit Ingenuus as an acolyte, probably reasoning that if he would go to such an extreme in in interest of his family and his peers, perhaps he would go just as far in the interest of the Imperium if he was properly schooled. The identity of Ingenuus was erased, as much as it could be, and then he was subjected to intensive training by the Adeptus Ministorum. When it was done, he emerged as a loyal cleric of the God Emperor known as Solon Modrak. The mental reassignment didn't go perfectly however, and fragments of Ingenuus remain. For reasons that he can't fully explain, he feels a certain disregard for the various Planetary Defense Forces of the Imperium. Interestingly, and perhaps worryingly, the bit about the Damned Brotherhood wasn't something Solon was programmed with, his mind invented it independently. It is almost as if, on some level, he is aware of and wishes to atone for his past heresy.