I got the following info from a post KerfufflyKitty posted in the old forums back in January 2018. I think the info is very useful for those with Broadcom WiFi cards/chips, so I'm going to add the info to the new forums.
You'll need to temporarily use an ethernet cable.
(01) If you have just installed Solus, perform a system update either via the Software Center or drop to the command line and enter:
sudo eopkg up
If you use eopkg, answer yes if there are additional packages to be installed.
(02) Using Software Center, go to Applications - Hardware and install the applicable/appropriate Broadcom driver:
broadcom-sta-current is for the current Linux kernel
broadcom-sta is for the LTS Linux kernel
To determine what kernel you have, enter the following from the command line:
If the value for Kernel is higher than 4.9.x (as of Solus v3.9999), you have a current kernel.
To install using eopkg:
eopkg it broadcom-sta-current
eopkg it broadcom-sta
(03) From the command line, enter the following:
echo "install wl /sbin/modprobe cfg80211; /sbin/insmod /lib/modules/\$(/bin/uname -r)/kernel/drivers/net/wireless/wl.ko" | sudo tee /etc/modprobe.d/hackboot.conf
echo "wl" | sudo tee /etc/modules-load.d/wl.conf
(04) Restart the computer.
(05) Use the appropriate credentials to connect to your router using the NetworkManager Applet.