If you want the original DEM values between 1000 and 1255, why do you want to add 1000?
I will share with you the workflow I would follow to achieve this (but without adding the 1000). I like using Raster Functions as I can test the settings and I don't have to save the final output to disk.
From Imagery tab, open up Raster Functions and search for Calculator. Add you DEM as the Raster Variable and assign a character to it (like x in my below image).
Under Expression, Type in Con and hit enter to enter your conditional statement. Then you can type Con((x>=1000)&(x<=1255) , x , 0 ). I was not sure whether your highest pint is 1255 or you only wanted to display that range. Then under the General tab, change the Output Pixel Type to values to 16 Bit Unsigned, then hit the Create new layer at bottom of pane.
As Jayanta pointed out, your DEM is unlikely to be a 8 Bit Unsigned type as the values are greater than 255. I also noted from your image that it has 3 bands. Are you displaying the properties for the DEM you want to work with? Similarly, the output of the Raster Function cant be a 8 But but rather a 16 Bit type to show values greater than 255.
If you want to add 1000 to teh DEM values then you modify the Con statement to something like:
Con((x>=1000)&(x<=1255) , x+1000 , 0 )