I suppose I read this story in a book in the nineties but I have no memory of actually reading it or the cover, I just remember a lot of the plot.
Scientists find out they are being contacted by the inhabitants of some other universe. I believe this happens by one element being exchanged with another (I remember wolfram was involved because I had never heard that word before) and messages somehow added. This leads to earth building some sort of machine together with the other universe (it is the description of this machine that I really would like to read again) that somehow generates energy on both sides. Only later do the people on earth realize, that it also slowly changes some of natures constants, threatening, I believe, the sun.
The book also had detailed descriptions of everyday life in both universes. I remember some sport played in the lower gravity of the moon and the aliens having three distinctive sexes.