Hi,
Thanks for the interest in our plugins.
I can help out here.
We have the Community Event Plugin for Front End Editing.
It does not work as you describe though as it creates a form you can use to create events.
You can read about how it works here:
New User Primer: Community Events
Please not it only requires the core version of the Events Calendar found for free on WordPress.org: https://wordpress.org/plugins/the-events-calendar/ and does not require Pro to work.
Also, out of the box if you are logged in and your theme does not remove the admin bar you can click edit in the bar when viewing any single event.
Let me know if you have any follow up questions.
Thanks