First let's address the framing of your question. You asked about emotional intelligence. Theories of multiple intelligences are not universally accepted or well replicated findings in psychometrics. You should expect that generally intelligent people will also be good at dealing with people. The idea that smart people are often lopsided or lack "people skills" is not supported by psychometric data. The next thing to…
"Emotional Intelligence" is just a marketing term for awareness of other people's emotional needs/thoughts/behaviour/etc. and modulating one's interactions accordingly.
The trick is to do it effectively without allowing oneself to be manipulated/becoming a doormat/hurting the other person's ego.
The books Crucial Conversations and Crucial Confrontations by Kerry Patterson et al. are useful in this regard.