ES File Explorer used to do this and I loved it! Install ES File Explorer on both my phone and nVidia Shield, then easily remotely sideload apps with apk files from my phone/tablet.

Of course it's a PITA now that ES File Explorer isn't readily available on the Play Store, so I've tried a couple other popular file explorers, but I haven't found one with that feature.

I honestly don't care if it's a file explorer app or not... I just want that particular feature. If I have to pay for a premium version, that's fine by me.

Any help will be greatly appreciated.