YES! it is POSSIBLE
I have no idea why people comment just for the sake of commenting! Makes me sick!
Anyway, You sign into your google account. Follow these steps -
1) Go to blogger (To the blog which you want to give access to other person)
2) Go to settings >> Basics
3) Scroll to 'Permissions'
4) Add the gmail ID of the person you want to give access to your blogs. In this case invite this person as 'Moderator/Author' that will allow him/her to edit and add posts to your blog.
5) This invitation expires in 24 hours so ask that person to accept it.
Note: If that person asks you to make him/her 'Admin' Don't do it, since they can delete/remove you as admin!