I got it to work. I had to re-download Discord: https://discordapp.com/download, then run these commands:
sudo dpkg -i discord-0.0.5.deb:
root@adam-desktop:/home/adam/Downloads# dpkg -i discord-0.0.5.deb
Selecting previously unselected package discord.
(Reading database ... 253573 files and directories currently installed.)
Preparing to unpack discord-0.0.5.deb ...
Unpacking discord (0.0.5) ...
dpkg: dependency problems prevent configuration of discord:
discord depends on libc++1; however:
Package libc++1 is not installed.
dpkg: error processing package discord (--install):
dependency problems - leaving unconfigured
Processing triggers for desktop-file-utils (0.23-1ubuntu3.18.04.1) ...
Processing triggers for gnome-menus (3.13.3-11ubuntu1) ...
Processing triggers for mime-support (3.60ubuntu1) ...
Errors were encountered while processing:
Notice the error, so run the next command:
sudo apt-get install -f:
root@adam-desktop:/home/adam/Downloads# apt-get install -f
Reading package lists... Done
Building dependency tree
Reading state information... Done
Correcting dependencies... Done
The following additional packages will be installed:
The following NEW packages will be installed:
0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded.
1 not fully installed or removed.
Need to get 240 kB of archives.
After this operation, 1,024 kB of additional disk space will be used.
Do you want to continue? [Y/n] y
Get:1 http://us.archive.ubuntu.com/ubuntu bionic/universe amd64 libc++abi1 amd64 6.0-2 [56.7 kB]
Get:2 http://us.archive.ubuntu.com/ubuntu bionic/universe amd64 libc++1 amd64 6.0-2 [183 kB]
Fetched 240 kB in 0s (781 kB/s)
Selecting previously unselected package libc++abi1:amd64.
(Reading database ... 253662 files and directories currently installed.)
Preparing to unpack .../libc++abi1_6.0-2_amd64.deb ...
Unpacking libc++abi1:amd64 (6.0-2) ...
Selecting previously unselected package libc++1:amd64.
Preparing to unpack .../libc++1_6.0-2_amd64.deb ...
Unpacking libc++1:amd64 (6.0-2) ...
Setting up libc++abi1:amd64 (6.0-2) ...
Processing triggers for libc-bin (2.27-3ubuntu1) ...
Setting up libc++1:amd64 (6.0-2) ...
Setting up discord (0.0.5) ...
Processing triggers for libc-bin (2.27-3ubuntu1) ..