Logansdad - If you have a digital image of, say, 4749 x 3167, it's 4749 pixels wide x 3167 pixels vertical. It isn't actually "at 240dpi" - but you could print it at 240dpi - or 300dpi, so on. Some printer applications will resample to print, but aren't always very accurate.
At printer 240dpi that image will print at 19.78" x 13.19" - call it 19.8 x 13.2, in inches. At printer 300dpi it would be 15.83" x 10.55".
Either way, the AR (Aspect Ratio) is very close to 3:2 - so it's probably from a DSLR. P&S images are mostly 4:3, though some higher end P&S cameras also offer 3:2, 16:9, and a few, 1:1.
Your desired printout is 8 x 10 - which AR is 5:4. While Photoshop 'can' resample a 3:2 image to 5:4 - that would skew and ruin the content. That is, you can't resize Aspect Ratios without skewing the image.
You will have to crop, to get the 5:4 AR. In 3:2 the vertical is 66% of the width, in 5:4 the vertical is 80% of the width. So you can see which way the cropping has to go. Only you know the content of that image, and how it was composed, to decide whether the crop will be at one edge only, or partly at that edge and partly at the opposite edge.
You say, "raw tif" - do you mean a TIFF image exported from RAW processing? If so - that's already the best quality, in a lossless format. Changing to JPEG, which is a "lossy" format, will degrade the image slightly. If your printer can't handle TIFF, you have Photoshop - so convert the TIFF to PSD, which is a very good non-lossy format native to the Adobe programs.
Almost any printer will take PSD as the output feed from Photoshop.
Once you have your 5:4 image AR, you'll need to decide whether to use the printer's resampling to get the actual 10 x 8 printout size - or use Photoshop to resample. Photoshop is by far the best at resampling - the program has been in the advanced imaging business for quite some time. Use the Bicubic option, it's most accurate.
For a printout at 8 x 10 at 240dpi, without printer resampling, the image will be 1920 x 2400.