What is the exact difference between "keep silent" and "keep silence"?
Where did you see keep silence? We user maintain (radio) silence when -people are not allowed to use radios and other communication.
"Keep silent" means "Remain silent"
"Keep silence" means "Maintain silence"
The exact difference is that the first uses the adjective (from "silence") and the second the noun. There are no other exact differences without a context.
PS: If a football goalkeeper was putting his team off by making too much noise, he could be asked to "keep silently".