You can download the appropriate driver using the live media since wifi works that way... You will need to know what kernel is currently installed on your Manjaro Gnome installation.
uname -rTells you what kernel you are running. Now... while booted in the live media, open a terminal and run:
pacman -Ss broadcomyou will get a list of the available broadcom packages for the different Manjaro kernels. You can download one of those listed packages by running
sudo pacman -Sw linux419-broadcom-wlthe -Sw switch for pacman only downloads and does not install the package... Your downloaded package will be in /var/cache/pacman/pkg and you can copy it to any convenient location. You can now boot back into your Manjaro Gnome and you can install the package from where you copied the file to with:
sudo pacman -U linux419-broadcom-wlIn my case I chose linux419-broadcom-wl because my kernel is 419 but yours might be 414, so it is always a good idea to check this before downloading...
After installation and a reboot your wifi should be working as expected.