First thing to know is that the electronic image and the paper image will never look the same, never ever. The mediums are as fundamentally different.
A couple ideas.
1 - The scanner and the paper have different "ranges" that need to be adjusted. Simply put the scanner doesn't see the paper as white or your deepest shadows as black. I don't use the scanner's "auto" settings for this correction. Once it is scanned, you can use any image editing software you please to set the black point and white point. (Some software packages have a dedicated function for this others use curves or levels or ...) This will probably fix about 80-90% of your problem.
2 - The second major problem is that of sizing and sharpening. To understand this problem you need to understand that the unit of measure that matters is "a pixel".
PIXELS PER INCH (ppi and similarly dpi) IS ONLY A CONVERSION FACTOR NOT A MEASUREMENT.
Scanning an 8x10 at 300ppi gets you an image that is 2400 pixels down one edge (8x300) and 3000 pixels down the other (10x300).
The finished images you can display here at APUG are no larger than 850x750 pixels. (Notice, there is nothing there about "inches")
Computer monitors can only display a fixed number of pixels/dots i.e. 1024x768 and the ppi/dpi will normally be say 96 or 72, not 300.
Your 2400x3000 pixel (8x10) will display on my computer screen at 25"x31.25" at it's "natural" screen resolution of 96 ppi laptop, even bigger on my 72 ppi CRT. So I won't be able to see the whole picture on the screen at 100%. There simply are not enough dots on a normal monitor to do it.
As we scrunch our 2400x3000 pixel images down to be able to see the whole picture our computers start averaging and guessing to display an image "close" to ours. This process is riddled with averaging errors that lead to lousy looking stuff.
The best you can do, once you have set you B&W points is to use your editing software to re-size the image to no larger than 850x750 pixels. View the image at exactly 100%, no more, no less, and set your sharpening to your taste.