Generally speaking, the main things you have to check is the socket type, and that the motherboard actually supports that type of processor (sometimes a bios Flash update is required, other times a whole new motherboard is the only option)
However, in your situation there is a problem:
The E1-2500 is a BGA769 (FT3) APU, based on Kabini core. BGA = Ball Grid Array. This type of 'socket' is used to permanently attach a processor to its motherboard during production, making future upgrades impossible.
In other words, to upgrade your laptop, you will need to get a whole new motherboard/APU combo that was designed for your particular laptop series.