Should be quite easy doing =IF(F2>E2;"SUCCESS";"ERROR")
You can omit the "SUCCESS" and you only display the error should it fail. This will work as long as the fields are actually formatted as a proper date.
Updated code:
=IF(AND(NUMBERBLANK(E2:F2)=0;F2<E2);"ERROR";"")
What this does is: Check if both cells are filled, if they are chech if E is smaller than F, and write ERROR if that is the case.
To do this for the entire column you need to replicate the formula. For existing dates, just double click the lower right knob in the cell the formula is, and it SHOULD replicate down till the end of the row (if the row is next to the date). Other than that, just pull the knob down as far as you need it.