In Foundation and Earth, there is a story about a Settler man and a Spacer woman leaving Solaria together. However, there is no further explanation in the book. Is it explained in another book?
Robots and Empire tells the story of D.G. Baley, a settler, and Gladia Delmarre, a Spacer, originally from Solaria. They didn't meet on Solaria, but they visited the place together. The Wikipedia entry for Gladia Delmarre states that her story is indeed the one referenced in Foundation and Earth. According to the robots and spacers series, this is probably the only relationship between a Solarian and a non-Spacer ever anyway, as Solarians were extreme isolationists.
Robots and Empire establishes the connection between the Robots universe and the Foundation universe, setting a basis for the later Foundation stories. I think it is best read in sequence after the other three robots and spacers novels.
I've always assumed this was probably a garbled reference to (Asimov's 1957 sequel to 'The Caves of Steel') 'The Naked Sun', in which Plainclothesman Elija Baley arrives on Solaria from Earth to investigate the murder of Gladia Delmarre's husband. They established a strong relationship and while they did not leave Solaria together, they both left Solaria at about the same time, and popular dramatizations of the episode played up the relationship to the point that most people probably thought they left together. Note that this story takes place thousands of years in the past by the time it is referred to in 'Foundation and Earth.'