To Kill The Ghost
How's your conjuration skill? Nothing makes a fight easier than summoning something to fight for you, or at the very least to take a few hits before going down so that you don't have to. If you don't have the conjuration/magicka for a summon, but still have a decent conjuration skill, invest in a spell with the "Turn Undead" spell effect. There are various places you can get it, but I believe the easiest is probably from Rominous Polus, in the arch mage's tower lobby, arcane university, imperial city. These will cause the undead (up to a certain level, which is dependent on what type of spell you bought) to run in fear of you, which is a great way to win a hard fight, just keep hitting him in the back until he goes down. If none of that is an option, you need to buy a silver weapon (the best defense or a fighting chance in the imperial city market district probably has them, or any other weapons and armor shop you like using) and just hack away until you kill it, don't be afraid to drink some health potions if you need too (which are found at apothecary shops all over the game, like "The Golden Carafe" in the imperial city market district, if you didn't already know). I know some people told you to get an enchanted weapon, but with the undead, that's usually not a good idea unless you're just dealing with a skeleton or a zombie. Ghosts, and especially Liches (which you'll meet at higher levels) have a tendency to reflect spell damage (like the kind caused by an enchanted weapon) back at you, which will make a lot of fights more difficult than they need to be. If none of that works, try going to the "Warlock's Luck" shop in Bravil (which is the town you got that quest from I believe) and buy some scrolls. Scrolls that summon creatures, scrolls that do damage (again though, ghosts can reflect this sometimes, so be careful), whatever you think you'll need, and try again. Also, if you do end up using enchanted weapons/spells/scrolls, remember to avoid frost effects, the undead can shrug those off, and shock isn't that great either, you want fire. The undead have a 50% or more weakness to fire depending on what creature you're talking about, ALL OF THEM, so always use fire damage against them.