NOTE This package should probably be unnecessary. I was mostly able to replicate this using the built-in desktop-save-mode and this config:

(setq desktop-globals-to-save '()
      desktop-files-not-to-save ".*"
      desktop-buffers-not-to-save ".*"
      desktop-save t)
(when (window-system)
  (desktop-save-mode)
  (desktop-read))

Unfortunately, the size saved is slightly different than the size restored, so I still use this package and the restore-frame-position-dimension-tweak variable.

restore-frame-position

Remember and restore initial frame position when restarting Emacs.

Based on various snippets around the internet, including this one which was the oldest I could find.

Installation

You can install this package from Melpa

M-x package-install RET restore-frame-position RET

Usage

Add to your init.el:

(restore-frame-position)

Adjust restore-frame-position-dimension-tweak so that you end up with the exact size after restarting as you had before you restarted. If any one knows how to calculate this, I'd be grateful if you could tell me.