It could not have been more improbable or unexpected. It was as if a messenger from Allah had descended to the Promised Land on a magic carpet.
At two minutes to 8 on Saturday night—the evening arrival was carefully chosen so as not to violate the Jewish Sabbath—the Egyptian white Boeing 707, its red trim glistening under klieg lights, rolled to a stop at Tel Aviv's Ben Gurion Airport. Israeli army trumpeters blared out a welcoming fanfare. As thousands of Israelis waved their newly purchased red-white-and-black Egyptian flags, out stepped President Anwar Sadat on a "sacred mission"—to speak directly to...