The story is told in the first person. The telepath finds his ability more an affliction than a gift, because he finds people can be overwhelming. He yearns to meet another telepath, hoping at least to have someone who would at least share his problem and could commiserate. When he does, the reader could imagine for a moment that it is turning into a 'boy meets girl' story. Instead, they both realize the sheer awfulness of complete loss of privacy, and I think the story ends with them shouting 'get out, get out' at each other.
I read this between 1970 and 1974, but of course it could have been printed earlier. But it does mention World War II, so not pre-war.
I was convinced that it was by Poul Anderson, but I've raked through everything I could find, without luck.