I read this short story in the 1960s — can't remember just where. The main character is a middle-aged man, who, if I remember correctly, carries a cane. He is a telepath who was almost driven insane by the flood of other people's thoughts and emotions but eventually, with great difficulty, learned to stand it. (I think he believes himself to be the only telepath in the world.) He comes across a young man whose telepathic ability has just manifested itself; convinced the young man won't be able to stand it, the main character kills him!
Thanks in advance for any help you can give me.