I'm not quite sure when it was made, but I bought a Kenmore 158.14001 in 1969.
Google the make and model number
You may find one in your local appliance parts store, or on internet
Manufactured around 1997 I believe.
Open the door, theres a plate on the right side frame, inside.
I purchased this machine in 1979
The phone number of the Kenmore Library is: 425-486-8747.
The phone number of the Kenmore Heritage Society is: 425-488-2818.
I have one and there are some numbers on it that may be a manufacturing date. My washer may be manufactured in 1960.
Kenmore dryers have been available for many years. With a specific model number and a call to a Sears appliance repair center, you can probably get the information you need. Without that model number, it's anyone's guess when it was manufactured.
I still own and operate my Kenmore Sewing Machine, Model Number 1931 (158.19310). It was my Christmas gift the first year I was married in 1976!
The phone number of the Kenmore Association is: 703-373-3381.