As an ILI who was recently in a relationship with an SEE, I may be able to provide some insight into this. SEE and ILI can meet one another through any of the normal means that people meet each other; in my case, it was introduction by a mutual friend. As far as how the relationships work out, this is my first relationship since learning socionics (and the SEE is actually the one who taught me about it), so I have only this one experience from which to draw examples. For me, I'm rather quiet and withdrawn most of the time. My SEE ex and I met at a party, and I was sitting in the corner generally ignoring the party, while she repeatedly tried to engage with me and I rebuffed her. It was only after the party, the next morning, when we woke up that I started to find her more interesting. I spoke to her on a one-to-one basis and was immediately attracted to her charm and spirit. A few weeks later, we started dating, and we did have quite a bit of difficulty, I will admit. The biggest problem we had was that I was interested in a long-term relationship, and she was not. The irony is that, even though, as an ILI, as you say, I'm supposed to value my alone time and such, I actually sought out way too much of her time, while she was much more interested in being alone. As often happens with ILIs, when we make attachments, we tend to make very strong attachments. Unfortunately for me, I was much more attached than she was, and so eventually she left me.

More directly to your question, I'm an educated, analytical man in every sense of the word. I'm a Master's student in Biology at the moment, and a former Air Force Intelligence analyst. It really was the vibrancy and energy of the SEE that drew me to her. It was her "life of the party" personality that was most attractive to me. She represented everything about the world that I had always lacked, a connection to other people and this sense of belonging that I didn't have, and could never find on my own. I can't answer for her side of what she found attractive about me, but at least from the point of view of your question, my experience seems fairly relevant.