The abbreviation "C.E." is a standard way of denoting dates in scholarly literature. C. E. means "Common Era" and B.C.E. denotes "Before the Common Era." The year 1 C.E. is the same as the year 1 A.D.
Many people do not appreciate the fact that the abbreviations AD and BC profess the Christian faith: Anno Domini, meaning "in the year of Our Lord", states the belief that Jesus is the Lord, and BC states that Jesus is the Christ (Messiah). Religious scholars, many of whom are non-Christian, are keenly aware of this, so a neutral way of denoting the year was devised.
Just like AD, the CE system counts the birth of Jesus as year 1.
In fact, we do not know what year Jesus was born. The Gospels indicate he was born near the end of the reign of Herod the Great. The AD system thus takes the last year of Herod's rule as the birth year of Jesus. Because of a counting error, this year turns out to be, in the modern calendar, 4 BC/BCE, not 1 AD/CE.
Not even scholar's appreciate the fact that our calendar does not count from the first year of Jesus, which is unknown, but from the last year of Herod, which is known. Thus the entire AD/BC system is based on the reign of the last great Jewish king!
My own proposal is that non-Christian scholars can indeed use AD and BC in good conscious, as long as they interpret AD to mean "After the Death of Herod" and BC to mean "Before Caesar", i.e., before the Jewish state was partitioned by Augustus Caesar upon the death of Herod.
- G. J. Goldberg