Just now my customer entered "+10" in a date-box which immediately responded by setting the date to today+10 days, so 15-06-2018. This works fine because the application is Baan, an ERP popular in the early 90's. Since I hate Mendix getting ridiculed because of Mendix can not do something that a very old app can so easy, I suggest this idea:
Make the date-picker accept smart entries like "+14", "-1"
+14 of course should result in today's date plus 14 days: 19-06-2018
-1 of course should result in yesterday: 4-06-2018
And also include Marnix' suggestions. +1 for his suggestions for improving usability.
Apart from responding to '+' or '-' in the inputbox, the dropdown of the datepicker can also use some extra buttons and options:
Currently the dropdown looks like this: http://www.tieka.nl/assets/dateNow.png
With the extra options it will look for instance like this: http://www.tieka.nl/assets/dateNew.png
Easier to immediately select the correct month by clicking in the serie 'J F M ... D'. Easier to go x unit forward in days, weeks, months or years.
Still not exactly sure though how the +10 interaction should be visualized, I guess it could be solved by a listener waiting for shift and the plus key to be pressed, then a small slide out input field which can be confirmed with enter or something could work.
Personally i think the entire date picker / time picker for Mendix should be reconstructed, I do believe this interaction is quite nice to have for separate date / time parts selected, so that when I select the day part of the date and do +10 it adds 10 days, if I select the month part and do +1 it adds a month. Same for minutes and hours.
Also I believe just using the arrow keys while having the date time part selected should increment and decrease accordingly or middle mouse scroll wheel.
Navigating between date parts should be doable using the tab key