How do I show date next to time in the panel with gnome-shell?

As a regular user run this in a terminal when using GNOME Shell:

gsettings set org.gnome.desktop.interface clock-show-date true

Not an ubuntu user but, if you install gnome-tweak-tool, you'll have a nice gui to adjust things like this.

I'm guessing your install from repo might be something like:

apt-get install gnome-tweak-tool

For Ubuntu 17.10, I found using the gnome-tweak-tool to be the most convenient way.

• Install gnome-tweak-tool if not already installed.

   sudo apt install gnome-tweak-tool
  

• Start the tool, either from command line, $ gnome-tweak-tool or using Dash (tweak).

• Select Top Bar from left and then make the necessary changes at right under Clock.