Solomon was joint Deputy with Clarence Goodman in the earliest days of Justice Department. He was a far more politically minded man than his boss and when Fargo violated his own celibacy rules in 2051, Solomon pushed him to cover it up and carry on. When Fargo made a failed suicide attempt which left him severely injured, it was Solomon's idea to fake a heroic death for him as a public relations move.
He succeeded Fargo as Chief Judge until 2057, originally Chief Judge of the United States until he became Chief Judge of Mega-City One in 2052 after the Autonomy Act. He founded Psi Division at the end of his term of office in 2057.
In 2057, he became tired of the politics and handed the role over to Goodman Goodman]]. On his way out, he advised Goodman to build up Justice Department's arsenal due to concerns of Booth. Solomon still served as a senior Street Judge on the Council of Five and was advising action against Booth when the Atomic Wars suddenly broke out.
When Booth was deposed and arrested, it was Solomon who got around the Judge's qualms about executing the last president: the "Judgement of Solomon" sentenced Booth to 100 years of suspended animation, or what he called a "living death". Future generations would then sentence Booth properly with the benefit of hindsight. (Booth himself found the Judgement laughable, rhetorically asking "was that supposed to be some kind of terrible punishment?")
In 1977 nobody expected the Judge Dredd strip to last for more than a couple of years, so no concerted effort was made to establish a proper character history or backstory until later on. Before Origins, there was debate among fans as to whether Solomon had ever been Chief Judge: he wasn't wearing the uniform and rank wasn't given, but he was sitting on an eagle throne and passing judgement.
A feature published in the 2000 AD Annual 1984, giving an unofficial timeline for future America, stated that Solomon reigned between 2051 to 2058. (The date of Solomon's resignation was deduced from a statement in prog 89 that Goodman had ruled for 43 years, ending in 2101.) This timeline was later adopted for the Judge Dredd Roleplaying Game. Other fans pointed out that these dates contradicted the date of 2070 given in the Cursed Earth story, that the timeline was not written by any of the Dredd strip writers and was indeed entitled an "Unofficial Version" (and invited readers to submit their own versions), and that the feature had been superseded by Oz. This story showed a flashback to 2070 with Fargo (in his first strip appearance) as the absolute ruler of America, implying that Solomon was not chief judge when he sentenced Booth.
Origins would reconcile most of these facts by showing Fargo's death being faked in 2051, while he still secretly survived into 2070. Solomon succeeded him as chief judge, and was in turn succeeded by Goodman in 2057.