Extracting a text from one cell to reference another sheet

Hello! I'm trying to extract information from a different sheet within the same workbook. When looking at the attached example in the images below, the simple equation I would use is...

=Cleveland!A1         which spits out "Browns"

But with what I'm doing in a personal work related excel sheet (I'd share it but not allowed to), I need to extract information in a different sheet (like the example above) but want to specify the sheet name in a cell itself. Wording if funky but for example, instead of manually typing "Cleveland" into the equation, =Cleveland!A1, I want to reference the cell that says the sheet name of "Cleveland". 

Cell E3 = Cleveland

Cell E4 = 'E3'!A1        does not work.

Any way to modify that equation a bit to make it work? Would save a lot of time in the sheet I'm currently working on instead of manually typing each equation.