Line a baking sheet with wax paper and set aside. Hull the tamarind, removing the outer shell and inner strings to separate the fruit.
In a wide pan over medium heat, combine tamarind pulp, water, 1 ½ cups of the sugar and ½ teaspoon of the salt. Bring to a boil. Lower heat and continue to cook, stirring and mashing with back of spoon, for about 15 to 20 minutes or until mixture is very thick and sticky.
Using a teaspoon, scoop tamarind mixture and drop in a single layer on prepared baking sheet, leaving space between each mound. Refrigerate for about 1 to 2 hours or until completely cooled and slightly hardened.
On a wide platter, combine the remaining ½ cup sugar and ½ teaspoon salt.
Using palm of hands, shape each tamarind mound into balls. Roll in sugar and salt mixture to fully coat. To store for future use, wrap about three to four pieces in cellophane. You can also store in a covered container.