Simply boot any liveCD/USB and chroot into the installed F18 system. "grub-install /dev/sdb" should do the job - providing you hit the correct USB drive node. The cfg should be o.k. as-is seeing as you want to run the hard disk system once booted, but in need you can run grub2-mkconfig - Fedora doco
here.
N.B. - Fedora is a bit different to (for example) Ubuntu in its grub2 setup. Be careful using docs off the web that are (even unknowingly) heavily Debian-centric.