Family Sharing using iCloud

I have been trying to set up a Family Sharing under iCloud so that I can see where the members of the family are using Find My Friends app. Problem is there are only two of us and when I try to put in my wife's name or email address I get an error notice that I can not include myself, as only my name is on the AT&T account for both phones. Any way to get around that? Or where am I going wrong as usually only one name is on a family sharing account. I have searched every where I can think of and can't find a simple answer, and I need it simple.
I go to settings, then iCloud, then Family, then Add Family Member, enter my wife's name, and get an error "You cannot send an invitation to your own account" Don't most accounts for a family plan only have one name on the account?
Thanks for all who can help.

If both you and your wife are using the same account, then you can not turn on family sharing. I have both my and my wife's iPhones set under one account, one Apple ID. So like you, I can not turn on family sharing. Members of your family would need their own Apple ID (account) in order to send an invite for family sharing.

Your reply makes sense to me and that is why I can't invite myself to join. I am going to set up another apple/icloud account for her phone. Thanks for your reply.

Just now tried turning on Family Sharing and it worked and found something I did not realize. When you create an iCloud account, it also, apparently, creates an AppleID for that account.

My wife and I use the same AppleID on our computers, phones, etc for all purchases and everything else.
We did, however, set her up with a separate iCloud account (because I had been using the .mac and .me accounts as my email account for some time prior) so that I got my mail and she got her mail.

Just tried setting up the Family Sharing to see if we could use her iCloud account (vs an AppleID) and found that Apple had created an AppleID for her with the same login credentials as her iCloud account.

Also, you do not need the 'Find my friends' app - nor do you need another AppleID/iCloud account to locate your wife if she is using an iPhone or Mac and is also using the same AppleID - you log in to your iCloud account on your Mac or use the "Find My Phone" app on the iPhone to locate all the devices using that AppleID.