I have my Sales cloud org connected and configured with the Marketing cloud Org. How can we send a Marketing Cloud email from Sales cloud using apex code and not from Marketing cloud connector?
You'll need a triggered send:
This link has plenty of information on setting up a trigger and configureing the send. This does require that you have the marketing cloud connector installed as it sends through the connector but doesn't require you to send the email manually through the UI. You can trigger the send via apex.