This Works!
% Button pushed function: SubmitButton
        function SubmitButtonPushed(app, event)
            filename = 'ArticleRequest.xlsx'; %file
            newEmail = {app.TextArea_Email.Value}; %data           
            Emails = readcell('ArticleRequest.xlsx','Range','Var1'); % read in emails
            % append new row to emails array
            Emails = [Emails; newEmail]; % append new email to list of emails           
            writecell(Emails,filename);  % write it to file 
            app.TextArea_Email.Value = 'Press <Next> to continue.';
            app.SubmitButton.Visible = 'off';
            uiconfirm(app.UIFigure,{'The file has been created.','Click OK'},'File Creation Confirmation','Icon','Success');
            app.NextButton_Email.Enable = 'on';
        end

