How do I use `sudo -e` together with gvim?

So when one edits a file owned by root it is recommended to use sudo -e. This will open a copy of the file in your favorite $EDITOR. Using this together with vim works like a charm.

However, when I want to use the graphical variant, i.e. gvim, it will open an empty file, and the sudo command returns directly, stating that nothing was changed.

Is there a way to make this work?

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