Verbal and written languages were created for this purpose. There are probably around 6000-7000 known languages in the world. Then we have art which always supplemented these to express the more elusive. A day might come when technology can recreate the mental/emotional states we experience. I wonder if language would even be necessary in that case. Maybe as shown in the TV series “doctor who”, satellite 5 episode, we could just access a portal of all shared experiences logged.
I think the reason for all the forms of communication we have today is because of this subjective reality each one of us lives in. That is probably the origin of art too, which tries to express things and feelings that are beyond verbal and mathematical languages. We are deeply interested in knowing what it feels like to be another person. We innately want to be one with everything. Sex probably comes the closest to feeling one with another human and imagining what it feels like to be them.