Here's a Java program that adds two dates:

import java.time.LocalDate;
import java.time.format.DateTimeFormatter;

public class DateAddition {
    public static void main(String[] args) {
        // Create two date objects
        LocalDate date1 = LocalDate.parse("2022-02-15", DateTimeFormatter.ISO_DATE);
        LocalDate date2 = LocalDate.parse("2023-02-16", DateTimeFormatter.ISO_DATE);

        // Add the two dates
        LocalDate result = date1.plusDays(date2.getDayOfMonth()).plusMonths(date2.getMonthValue()).plusYears(date2.getYear());

        // Print the result
        System.out.println("Result: " + result.format(DateTimeFormatter.ISO_DATE));
    }
}

In this program, we use the java.time.LocalDate class to represent the two dates. We create two LocalDate objects using the parse method of the DateTimeFormatter class, which allows us to convert strings into dates. We then use the plusDays, plusMonths, and plusYears methods of the LocalDate class to add the two dates together, and store the result in a new LocalDate object.

Finally, we use the format method of the DateTimeFormatter class to convert the resulting LocalDate object back into a string in ISO date format, which we print to the console.