Can you get out of a lease that you signed only 2 days earlier?

Unfortunately, this situation does not entitle you to terminate your lease early A lease is a contract. Additionally and there is no right of rescission for a lease.  However, in handling this situation a face-to-face meeting will be best.  Under the circumstances you are still liable for the remaining rental payments until the end of the lease term.  However, the landlord is under a duty to "mitigate damages". This means that he/she must use reasonable efforts to find a new tenant.  If so, you are then relieved of any further rental obligation.

Perhaps, you know of someone who would like to move-in?  This certainly would solve your dilemma.  Ask around, see if any family, friends, former co-workers, etc. might be acceptable replacement tenants.  Also, ask if you can sub-let the unit; in effect you then would  become the "landlord".  Under the circumstances, you could charge the sub-tenant less than what you are supposed to pay but at least it would give some financial relief.  Something is better than nothing.  Again, you would most likely need your landlord's permission to do this.  But it's a possible option here. 

Unfortunately, there is no right to get out of a lease signed 2 days ago. As soon as you sign a lease, it is binding; therefore, whether it is 2 minutes, 2 days, or 2 months later, you are obligated to unless there was some term in the lease itself giving you some period of time to rescind (i.e. ca cancel) the lease.

Similarly, whether or not the reason you want to rescind--relocation for  a job--is a good one doesn't matter; the landlord doesn't have to let you out for that reason.

You may wish to consider subletting or assigning the lease to someone else. The former would keep you obligated, but provide a subtenant to pay you money; that latter would get someone else to take the lease over from you. You need to check the lease first to see if either or both is an option.