When British Prime Minister Theresa May triggered Article 50 this week, the formal process began of separating what two things?

Theresa May, the British Prime Minister, confirmed that the UK had triggered Article 50 of the Lisbon Treaty, beginning a legal process that must end in two years' time with Britain leaving the EU. "This is an historic moment for which there can be no turning back. Britain is leaving the European Union," May told the House of Commons in London. A few minutes earlier in Brussels, the British Permanent Representative to the EU, Sir Tim Barrow, delivered a six-page formal letter of notification to Donald Tusk, the President of the European Council, in Brussels.