The key culprit in your Explorer’s performance is your vehicle’s transmission fluid. It is, more than likely low. The reason you can suspect this is that since your vehicle seems to run correctly and then seems to try to go into gear but then slips out, it is likely that the turbines within the tranny are circulating something but there is not enough to cover the vanes so the clutch packs would be activated. You can easily check the transmission fluid level by first looking at the owner’s manual to find the location of the transmission dipstick. Once you find it, pull it out quickly and wipe it with a clean rag, then reinsert it into the tube from which you withdrew it. On pulling it out again, check the level and the chances are good you will see the dipstick indicates that your transmission needs a bit of fluid.
Notice there are two sets of indicator marks on the dipstick, one for a hot reading and the other for a cool reading. If your vehicle is either running or very warm, use the hot reading. If your Explorer has just been parked for a bit, use the cold or cool indicator.
One other thing to notice is that you will likely see a large smudge on one side of the dipstick. This is caused by inserting it into the filler tube and then pulling it out. Make sure you read the side of the dipstick with the non-smudged mark.
If you are certain that the transmission fluid is low, then replace the amount that your SUV is missing.
Here’s something to consider: why is the transmission fluid low? If the fluid is down then it is a good idea to try to find the cause. First, look on all of the seams of the transmission itself to make sure there are no leaks. Look closely to see if you can detect any defects in the casing such as a hairline crack. You might try shining a black light on the tranny to see if there are any leaks. Next, check any seals on the differential and half-shafts to ensure that they are not leaking. Also be sure to check any boots to make sure they are performing their functions correctly. If everything seems okay, it is a good idea to check the feel of the fluid by rubbing your fingers together. If the fluid is gritty it may contain tiny metal fragments that indicate the the transmission has problems. Look at the color, as well, to be sure that it is on the pink side of things. If it is brown or black and has a burned smell then it is likely there has been some metal-on-metal grinding, possibly in the gearing, that indicates there are serious problems going on. Finally, check to make sure the transmission filter isn’t plugged up, holding back the fluid. This will make it appear the fluid is low. If you check things and haven’t found a problem, replace the missing fluid. Be sure to check the owner’s manual to determine the brand and purchase only the brand recommended by the manufacturer as the tranny was developed with that particular fluid in mind.
Be aware, though, that there may be problems brewing and it is a good idea to keep a close eye on the transmission for future issues.