The SQL Server 2014 Management Studio answer

SSMS 2014 relies upon the Microsoft Visual Studio 2010 Shell (Isolated) Redistributable Package. If this is uninstalled, SSMS will produce the error message ‘Cannot find one or more components. Please re install the application’. This can be corrected by:

1. Reinstalling the VS 2010 Shell from here: https://visualstudio.microsoft.com/vs/older-downloads/isolated-shell/
2. Try opening SSMS again. If it still gives the error, then:
3. Run Repair in SQL Server (2014) Setup

The SQL Server 2016 Management Studio answer

SSMS 2016 relies upon the Microsoft Visual Studio 2015 Shell (Isolated) Redistributable Package. If this is uninstalled, SSMS will produce the error message ‘Cannot find one or more components. Please re install the application’. This can be corrected by reinstalling VS 2015 or by installing the Microsoft Visual Studio 2015 Shell (Isolated) Redistributable Package.