The Dragons threatened a dramatic comeback when Ross Wardle's 73rd-minute converted score pulled the hosts to within four points.
But Edinburgh closed out the victory and as a result, Solomons is bullish about the rest of the season.
"Winning away is a sign this side is beginning to form and losing a man made it particularly difficult," he told the Herald.
"We have a tough run-in but this team is getting together nicely. They play for each other, there is a great vibe in the team.
"It was an exciting finish and a tremendous win. You have to remember there was a lot of pressure on us coming into the game and this was a lot about character and we were tremendous.
"We had to play the last nine minutes with 14 men but I thought we deserved to win."
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