Welcome to PowerApps,
In your case, You can use variables, as I understood you worked on 2 screens so you have to create a global variable 
Create a global  variable using the set function  for example the variable name will be "Inputvar1" then write this formula in  the OnStart property of the app
Set(Inputvar1,"text")
 
 
2. In the default property  "or the text property" of your textinput  set it with the variable, "just write the variable name"
3. in the Onselect property of your button update the value of the variable with your formula that you want the button to do.
For example  in the Onselect  property  of the button write the formula
set(Inputvar1,DatePicker.SelectedDate}) 

Finally, if you want to navigate to screen2 add this to the previous formula and you will see that the text updated with your variable