Larry,
I will try to restate the solution given by OR_CD in a different way that may be clearer for you.
First, go to System Preferences, and select the iCloud icon. A window will appear showing a list of applications, e.g., Photos, Mail, Contacts, Calendars, etc. There should be a check mark next to "Mail". Un-check it, wait a few seconds, then check it again.
Now, go to your Mail program / application. Under the bold "Mail" heading, bring the pulldown list including "Preferences". Click on Preferences. Click on the top icon "Accounts". On the window that appears, you should see a heading "Outgoing Mail Server (SMTP)". Next to that heading there is a pull-down list, and when you open it (hopefully) you will now see "iCloud". Click on that and be sure when the pull-down list goes away that you still see "iCloud" next to the heading "Outgoing Mail Server (SMTP)".
This should solve the outgoing mail problem. If you tried to send emails and they did not go out before, they may still be sitting in an outgoing mailbox. If they are not picked up and sent automatically, then select each one and send each one again by clicking on the "paper airplane" button. If that causes an error message to pop up saying that you don't have an outgoing mail server, within that error window you will have the option of selecting iCloud. Do that, and click on the button that says "Always use this server".
Now, if everything has gone out properly, the outgoing mailbox should be empty and (if you've configured your Mail program this way) there will be a copy saved in the Sent mailbox.