It's a supernatural ability. Supernatural abilities have no verbal, somatic (movement), focus or material components unless specifically mentioned in the ability's text.
In other words, if Channel Energy doesn't say it requires the cleric to speak, it doesn't require the cleric to speak. The only requirement listed in the ability entry is to be able to present a holy symbol, which is a somatic and divine focus component; no verbal component is mentioned. Channel Energy can be used in silence, even magically-enforced silence.