Sources extremely close to the alleged White House crasher tell us ... Michaele and Neal first met in 1998 -- while she was engaged to Tareq -- and the two felt an instant attraction.

We're told, Michaele and Neal managed to restrain themselves at first ... but in 2009, things came to a head -- and the relationship turned sexual. Michaele even bragged about the "wild sex" to friends through emails.

Michaele and Neal managed to keep the affair secret for the past two years ... but last week, things ramped up again ... and Michaele decided it was time to make a move.

As TMZ first reported, Michaele ditched Tareq on Tuesday to meet up with Schon -- and she's been with him ever since.