In conclusion:
No, you can't do that and no, you shouldn't do that.

Other than the fact that you can't just change them out, I want to point out the 2 cpus you listed.

You should not think that because the P340 has a higher clock speed, it means it's faster. For starters, the E1 has integrated graphics while the P340 does not. Comparing this further; An A8 APU vs the P340 (just an example.) While the P340 has a higher clock speed, the A8 has 2 more cores. Not only that but it is a newer technology compared to the P340 which means it might perform better than the P340 even if they both had 2 cores.

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BananaInChargeI'm guessing using the other laptop's GPU won't work on my motherboard then?

Depends on the motherboards. If BOTH motherboards have a slot to put the GPU on (if the GPU isn't soldered) then you can (sometimes). Thing is, your motherboard doesn't have an extra slot to put a GPU on. So yeah, don't even try it.

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BananaInChargeIt is possible to change components because I've seen it be done, I have friends who are way more into computers than I am and I've been around their house while they've been doing it.

It is possible, but only the same model. Have you seen them changing a motherboard/CPU of 2 different laptops then booting it up again, fully working?

Also, even if you can deal with changing the motherboard etc, you still need a GPU, which you can't get.

Long story short:

You cant.

Maybe if you are really lucky you can replace a gpu.

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You can't change a laptop's CPU. It's soldered in the motherboard (or at least most of the time) and changing it would be impossible without changing the whole motherboard. Thing is that, motherboards in laptops, except in the same range, are not interchangeable. This is because there is no such thing as a standard form factor for laptops. Also, the port layout (USB, VGA/DVI/HDMI, LAN, Memory card, eSATA, etc...) changes between laptop ranges, not just over time. They are all proprietary, each motherboard with it's port layout is designed and matched to a corresponding case and then sold as such

Yes, his CPU is not an APU, but there lies the problem: even if you manage to upgrade the CPU of your laptop, it's not going to work, because it has no GPU, means that it can't display anything on the screen.

Don't even think about buying a laptop GPU. Those are soldered into the motherboard too.

Give other info. Motherboard and power supply is what we need to know. Also you might need to get a seperate graphics card.