We switched from Slack to teams. Unfortunately the customer service here is terrible and does not want to help us. It is not possible to invite guests. We can not add a foreign email address to a team. We use Microsoft Office 365 and use the free version of teams. I'm happy about help. Thank you!
It is not possible to have Microsoft/Office 365 and Free Teams on the same tenant/organization. So maybe you confused about what you use. Maybe you have Microsoft/Office 365 licenses and these include Teams without an additional cost. Well, this is not called Free Teams, but just Teams.
You can find a number of threads about enabling guest access in Teams if you use search. In short, you must enable Guest Acces in Teams Admin Center (Org-wide settings > Guest access). This would allow adding addresses of already existing external users in your tenant to Teams. But if this user is not yet in your tenant, then you also have to enable this (regular Admin Center > Settings > Security & privacy > Let users add new guests to the organization). Or your admin would have to add every new external user manually in Azure portal.
Also, after changing these settings you may have to wait up to 24 hours before they take effect. And last advice. If this doesn't work in a team you already had, try creating new team and test. Sometimes setting change only propagates to new teams.