Etymology
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em- 
word-forming element meaning "put in or into, bring to a certain state," sometimes intensive, from French assimilation of en- "in, into" (see en- (1)) to following labial stop (-b-, -p-, and often -m-), or from the same development in later Latin in- (to im-). "This rule was not fully established in spelling before the 17th c." [OED], but it is likely the pronunciation shift was in Old French and Middle English and spelling was slow to conform. Also a living prefix in English used to form verbs from adjectives and nouns (embitter, embody). In words such as emancipate, emerge, emit, emotion the e- is a reduced form of Latin ex- (see ex-) before -m-.
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ex- 
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
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e- 

the later Romans evidently found words beginning in sc-, sp-, st- difficult or unpleasant to pronounce; in Late Latin forms begin to emerge in i- (such as ispatium, ispiritu), and from 5c. this shifted to e-. The development was carried into the Romanic languages, especially Old French, and the French words were modified further after 15c. by natural loss of -s- (the suppression being marked by an acute accent on the e-), while in other cases the word was formally corrected back to the Latin spelling (for example spécial). Hence French état for Old French estat for Latin status, etc. It also affected Romanic borrowings from Germanic (such as espy, eschew).

A different e- is a reduced form of Latin ex- before consonants (see ex-), and the e- in enough is an unfelt survival of an Old English alternative form of ge-.

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