Just facing the same issue and having to come up with a solution. I found that the files were still available on the server so I was able to use this approach.
Since the definition was deleted but the files are still on disk the way to get it back in there is simple. Create a definition J
On the page “Install additional modules” click “Create Module Definition” either from the near bottom of the page or from the Module Definitions menu (the little arrow pointing down).
In “Create Module Definition” fill in the fields “Module Name”, “Folder Name” with the text “FeedExplorer” and “Friendly Name” with “Feed Explorer”.
For description use “Allows users to browse RSS feeds using a tabbed user interface” (the original description).
Leave the rest of the items as is and click create.
Now the definition is created (somewhat). Towards the bottom of the “Edit Module Definition” module enter the text “Feed Explorer” in the field “New Definition” and click “Add Definition”.
Now the definition is created but not linked with any files just yet.
Towards the bottom of the “Edit Module Definition” module some new options have been added. Here you can link the existing files with the definition.
Click “Add Control”.
First add the FeedExplorer module by entering the following information (leave the rest as-is).
Source: “<None Specified>”
Textbox below: “Admin/Syndication/FeedExplorer.ascx”
Type: “View”
Click “Update”
Click “Add Control” (again)
Now we are adding the settings page for the feed explorer.
Key: Settings
Title: Feed Explorer Settings
Source: “<None Specified>”
Textbox below: “Admin/Syndication/FeedExplorerSettings.ascx”
Type: “Edit”
Now you have your feed explorer module back and it’s working :-)