Can I build a 12' by 18' shed with out digging holes for posts ?

You can use a cinder block footing to eliminate the need for hole digging. Something like this-https://www.silvatimber.co.uk/concrete-deck-pier-deck-block.html

http://www.finehomebuilding.com/2003/04/01/a-firm-foundation-for-a-backyard-shed

It would stand up to wear much better if the posts were dig into the ground. Are you physically unable? Or is there a restriction on digging on the property? If there are no restrictions you might want to see if someone can dig them for you so the structure has more stability

Rent a post hole digger for the day. Our harware rents out one.

The other question you need to answer is where you live. If you get high winds in your area, you need to make sure the roof material is "locked" down to the structure. Metal tie straps to the frame are good. Don't just use them at the corners.

Why not? You have to build on a level, so use patio/cement blocks to create the footprint of your shed and level according to need. then as you build your frame, erect the walls on the leveled corners. You could buy the cement blocks that will hold a 2" wide board (sold for building raised decks, etc.). Google, my dear, google!